[{"data":1,"prerenderedAt":6289},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fsteckbriefaufgaben":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fsteckbriefaufgaben":6276},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":556,"category":101,"checks":6163,"conditions":6193,"conditionsHtml":6194,"deprecated":6195,"description":6157,"extension":6196,"figure":6197,"figureCaption":6198,"figureHtml":6237,"formulaId":6238,"latex":6239,"latexHtml":6240,"level":6241,"meta":6242,"navigation":6207,"path":6243,"redirectFrom":6244,"related":6245,"seo":6250,"stem":6251,"subject":593,"summary":6252,"tags":6253,"variables":6258,"__hash__":6275},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fcalculus\u002Fsteckbriefaufgaben.md","Steckbriefaufgaben",[550,551,552,553,554,555],"Rekonstruktion von Funktionen","Funktionsgleichung aus Bedingungen bestimmen","Steckbrief Funktion","ganzrationale Funktion bestimmen","Bedingungen aufstellen Funktion 3. Grades","umgekehrte Kurvendiskussion",{"type":557,"value":558,"toc":6156},"minimark",[559,564,573,1034,1172,2477,2481,3004,3739,3960,4143,4896,5100,5432,5850,5854],[560,561,563],"h2",{"id":562},"erklärung","Erklärung",[565,566,567,568,572],"p",{},"Bei einer ",[569,570,571],"strong",{},"Steckbriefaufgabe"," ist nicht die Funktion gegeben, sondern ihre Eigenschaften. Gesucht ist der Funktionsterm, meist einer ganzrationalen Funktion. Man geht so vor:",[574,575,576,1013,1020,1027],"ol",{},[577,578,579,582,583,846,847,876,877,944,945,1012],"li",{},[569,580,581],{},"Ansatz"," mit allgemeinen Koeffizienten wählen, z.B. ",[584,585,588,662],"span",{"className":586},[587],"katex",[584,589,592],{"className":590},[591],"katex-mathml",[593,594,596],"math",{"xmlns":595},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[597,598,599,657],"semantics",{},[600,601,602,606,611,614,617,620,623,632,635,638,645,647,650,652,654],"mrow",{},[603,604,605],"mi",{},"f",[607,608,610],"mo",{"stretchy":609},"false","(",[603,612,613],{},"x",[607,615,616],{"stretchy":609},")",[607,618,619],{},"=",[603,621,622],{},"a",[624,625,626,628],"msup",{},[603,627,613],{},[629,630,631],"mn",{},"3",[607,633,634],{},"+",[603,636,637],{},"b",[624,639,640,642],{},[603,641,613],{},[629,643,644],{},"2",[607,646,634],{},[603,648,649],{},"c",[603,651,613],{},[607,653,634],{},[603,655,656],{},"d",[658,659,661],"annotation",{"encoding":660},"application\u002Fx-tex","f(x) = ax^3 + bx^2 + cx + d",[584,663,667,705,767,814,836],{"className":664,"ariaHidden":666},[665],"katex-html","true",[584,668,671,676,682,686,689,693,698,702],{"className":669},[670],"base",[584,672],{"className":673,"style":675},[674],"strut","height:1em;vertical-align:-0.25em;",[584,677,605],{"className":678,"style":681},[679,680],"mord","mathnormal","margin-right:0.1076em;",[584,683,610],{"className":684},[685],"mopen",[584,687,613],{"className":688},[679,680],[584,690,616],{"className":691},[692],"mclose",[584,694],{"className":695,"style":697},[696],"mspace","margin-right:0.2778em;",[584,699,619],{"className":700},[701],"mrel",[584,703],{"className":704,"style":697},[696],[584,706,708,712,715,756,760,764],{"className":707},[670],[584,709],{"className":710,"style":711},[674],"height:0.8974em;vertical-align:-0.0833em;",[584,713,622],{"className":714},[679,680],[584,716,718,721],{"className":717},[679],[584,719,613],{"className":720},[679,680],[584,722,725],{"className":723},[724],"msupsub",[584,726,729],{"className":727},[728],"vlist-t",[584,730,733],{"className":731},[732],"vlist-r",[584,734,738],{"className":735,"style":737},[736],"vlist","height:0.8141em;",[584,739,741,746],{"style":740},"top:-3.063em;margin-right:0.05em;",[584,742],{"className":743,"style":745},[744],"pstrut","height:2.7em;",[584,747,753],{"className":748},[749,750,751,752],"sizing","reset-size6","size3","mtight",[584,754,631],{"className":755},[679,752],[584,757],{"className":758,"style":759},[696],"margin-right:0.2222em;",[584,761,634],{"className":762},[763],"mbin",[584,765],{"className":766,"style":759},[696],[584,768,770,773,776,805,808,811],{"className":769},[670],[584,771],{"className":772,"style":711},[674],[584,774,637],{"className":775},[679,680],[584,777,779,782],{"className":778},[679],[584,780,613],{"className":781},[679,680],[584,783,785],{"className":784},[724],[584,786,788],{"className":787},[728],[584,789,791],{"className":790},[732],[584,792,794],{"className":793,"style":737},[736],[584,795,796,799],{"style":740},[584,797],{"className":798,"style":745},[744],[584,800,802],{"className":801},[749,750,751,752],[584,803,644],{"className":804},[679,752],[584,806],{"className":807,"style":759},[696],[584,809,634],{"className":810},[763],[584,812],{"className":813,"style":759},[696],[584,815,817,821,824,827,830,833],{"className":816},[670],[584,818],{"className":819,"style":820},[674],"height:0.6667em;vertical-align:-0.0833em;",[584,822,649],{"className":823},[679,680],[584,825,613],{"className":826},[679,680],[584,828],{"className":829,"style":759},[696],[584,831,634],{"className":832},[763],[584,834],{"className":835,"style":759},[696],[584,837,839,843],{"className":838},[670],[584,840],{"className":841,"style":842},[674],"height:0.6944em;",[584,844,656],{"className":845},[679,680]," für Grad ",[584,848,850,863],{"className":849},[587],[584,851,853],{"className":852},[591],[593,854,855],{"xmlns":595},[597,856,857,861],{},[600,858,859],{},[629,860,631],{},[658,862,631],{"encoding":660},[584,864,866],{"className":865,"ariaHidden":666},[665],[584,867,869,873],{"className":868},[670],[584,870],{"className":871,"style":872},[674],"height:0.6444em;",[584,874,631],{"className":875},[679],", und ",[584,878,880,901],{"className":879},[587],[584,881,883],{"className":882},[591],[593,884,885],{"xmlns":595},[597,886,887,898],{},[600,888,889],{},[624,890,891,893],{},[603,892,605],{},[607,894,897],{"mathvariant":895,"lspace":896,"rspace":896},"normal","0em","′",[658,899,900],{"encoding":660},"f'",[584,902,904],{"className":903,"ariaHidden":666},[665],[584,905,907,911],{"className":906},[670],[584,908],{"className":909,"style":910},[674],"height:0.9463em;vertical-align:-0.1944em;",[584,912,914,917],{"className":913},[679],[584,915,605],{"className":916,"style":681},[679,680],[584,918,920],{"className":919},[724],[584,921,923],{"className":922},[728],[584,924,926],{"className":925},[732],[584,927,930],{"className":928,"style":929},[736],"height:0.7519em;",[584,931,932,935],{"style":740},[584,933],{"className":934,"style":745},[744],[584,936,938],{"className":937},[749,750,751,752],[584,939,941],{"className":940},[679,752],[584,942,897],{"className":943},[679,752],", ",[584,946,948,970],{"className":947},[587],[584,949,951],{"className":950},[591],[593,952,953],{"xmlns":595},[597,954,955,967],{},[600,956,957],{},[624,958,959,961],{},[603,960,605],{},[600,962,963,965],{},[607,964,897],{"mathvariant":895},[607,966,897],{"mathvariant":895},[658,968,969],{"encoding":660},"f''",[584,971,973],{"className":972,"ariaHidden":666},[665],[584,974,976,979],{"className":975},[670],[584,977],{"className":978,"style":910},[674],[584,980,982,985],{"className":981},[679],[584,983,605],{"className":984,"style":681},[679,680],[584,986,988],{"className":987},[724],[584,989,991],{"className":990},[728],[584,992,994],{"className":993},[732],[584,995,997],{"className":996,"style":929},[736],[584,998,999,1002],{"style":740},[584,1000],{"className":1001,"style":745},[744],[584,1003,1005],{"className":1004},[749,750,751,752],[584,1006,1008],{"className":1007},[679,752],[584,1009,1011],{"className":1010},[679,752],"′′"," bilden.",[577,1014,1015,1016,1019],{},"Jede Eigenschaft in eine ",[569,1017,1018],{},"Gleichung"," übersetzen.",[577,1021,1022,1023,1026],{},"Das ",[569,1024,1025],{},"lineare Gleichungssystem"," lösen, z.B. mit dem Gauß-Algorithmus.",[577,1028,1029,1030,1033],{},"Den Funktionsterm angeben und die Eigenschaften ",[569,1031,1032],{},"überprüfen",".",[565,1035,1036,1037,1067,1068,1120,1121,1171],{},"Für eine Funktion vom Grad ",[584,1038,1040,1054],{"className":1039},[587],[584,1041,1043],{"className":1042},[591],[593,1044,1045],{"xmlns":595},[597,1046,1047,1052],{},[600,1048,1049],{},[603,1050,1051],{},"n",[658,1053,1051],{"encoding":660},[584,1055,1057],{"className":1056,"ariaHidden":666},[665],[584,1058,1060,1064],{"className":1059},[670],[584,1061],{"className":1062,"style":1063},[674],"height:0.4306em;",[584,1065,1051],{"className":1066},[679,680]," gibt es ",[584,1069,1071,1090],{"className":1070},[587],[584,1072,1074],{"className":1073},[591],[593,1075,1076],{"xmlns":595},[597,1077,1078,1087],{},[600,1079,1080,1082,1084],{},[603,1081,1051],{},[607,1083,634],{},[629,1085,1086],{},"1",[658,1088,1089],{"encoding":660},"n + 1",[584,1091,1093,1111],{"className":1092,"ariaHidden":666},[665],[584,1094,1096,1099,1102,1105,1108],{"className":1095},[670],[584,1097],{"className":1098,"style":820},[674],[584,1100,1051],{"className":1101},[679,680],[584,1103],{"className":1104,"style":759},[696],[584,1106,634],{"className":1107},[763],[584,1109],{"className":1110,"style":759},[696],[584,1112,1114,1117],{"className":1113},[670],[584,1115],{"className":1116,"style":872},[674],[584,1118,1086],{"className":1119},[679]," Koeffizienten, man braucht also ",[584,1122,1124,1141],{"className":1123},[587],[584,1125,1127],{"className":1126},[591],[593,1128,1129],{"xmlns":595},[597,1130,1131,1139],{},[600,1132,1133,1135,1137],{},[603,1134,1051],{},[607,1136,634],{},[629,1138,1086],{},[658,1140,1089],{"encoding":660},[584,1142,1144,1162],{"className":1143,"ariaHidden":666},[665],[584,1145,1147,1150,1153,1156,1159],{"className":1146},[670],[584,1148],{"className":1149,"style":820},[674],[584,1151,1051],{"className":1152},[679,680],[584,1154],{"className":1155,"style":759},[696],[584,1157,634],{"className":1158},[763],[584,1160],{"className":1161,"style":759},[696],[584,1163,1165,1168],{"className":1164},[670],[584,1166],{"className":1167,"style":872},[674],[584,1169,1086],{"className":1170},[679]," voneinander unabhängige Bedingungen. Übliche Übersetzungen:",[1173,1174,1175,1490,2011,2230,2474],"ul",{},[577,1176,1177,1178,1340,1341,1033],{},"Punkt ",[584,1179,1181,1218],{"className":1180},[587],[584,1182,1184],{"className":1183},[591],[593,1185,1186],{"xmlns":595},[597,1187,1188,1215],{},[600,1189,1190,1193,1195,1203,1206,1213],{},[603,1191,1192],{},"P",[607,1194,610],{"stretchy":609},[1196,1197,1198,1200],"msub",{},[603,1199,613],{},[629,1201,1202],{},"0",[607,1204,1205],{},"∣",[1196,1207,1208,1211],{},[603,1209,1210],{},"y",[629,1212,1202],{},[607,1214,616],{"stretchy":609},[658,1216,1217],{"encoding":660},"P(x_0 \\mid y_0)",[584,1219,1221,1289],{"className":1220,"ariaHidden":666},[665],[584,1222,1224,1227,1231,1234,1280,1283,1286],{"className":1223},[670],[584,1225],{"className":1226,"style":675},[674],[584,1228,1192],{"className":1229,"style":1230},[679,680],"margin-right:0.1389em;",[584,1232,610],{"className":1233},[685],[584,1235,1237,1240],{"className":1236},[679],[584,1238,613],{"className":1239},[679,680],[584,1241,1243],{"className":1242},[724],[584,1244,1247,1271],{"className":1245},[728,1246],"vlist-t2",[584,1248,1250,1266],{"className":1249},[732],[584,1251,1254],{"className":1252,"style":1253},[736],"height:0.3011em;",[584,1255,1257,1260],{"style":1256},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[584,1258],{"className":1259,"style":745},[744],[584,1261,1263],{"className":1262},[749,750,751,752],[584,1264,1202],{"className":1265},[679,752],[584,1267,1270],{"className":1268},[1269],"vlist-s","​",[584,1272,1274],{"className":1273},[732],[584,1275,1278],{"className":1276,"style":1277},[736],"height:0.15em;",[584,1279],{},[584,1281],{"className":1282,"style":697},[696],[584,1284,1205],{"className":1285},[701],[584,1287],{"className":1288,"style":697},[696],[584,1290,1292,1295,1337],{"className":1291},[670],[584,1293],{"className":1294,"style":675},[674],[584,1296,1298,1302],{"className":1297},[679],[584,1299,1210],{"className":1300,"style":1301},[679,680],"margin-right:0.0359em;",[584,1303,1305],{"className":1304},[724],[584,1306,1308,1329],{"className":1307},[728,1246],[584,1309,1311,1326],{"className":1310},[732],[584,1312,1314],{"className":1313,"style":1253},[736],[584,1315,1317,1320],{"style":1316},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[584,1318],{"className":1319,"style":745},[744],[584,1321,1323],{"className":1322},[749,750,751,752],[584,1324,1202],{"className":1325},[679,752],[584,1327,1270],{"className":1328},[1269],[584,1330,1332],{"className":1331},[732],[584,1333,1335],{"className":1334,"style":1277},[736],[584,1336],{},[584,1338,616],{"className":1339},[692]," auf dem Graphen: ",[584,1342,1344,1376],{"className":1343},[587],[584,1345,1347],{"className":1346},[591],[593,1348,1349],{"xmlns":595},[597,1350,1351,1373],{},[600,1352,1353,1355,1357,1363,1365,1367],{},[603,1354,605],{},[607,1356,610],{"stretchy":609},[1196,1358,1359,1361],{},[603,1360,613],{},[629,1362,1202],{},[607,1364,616],{"stretchy":609},[607,1366,619],{},[1196,1368,1369,1371],{},[603,1370,1210],{},[629,1372,1202],{},[658,1374,1375],{"encoding":660},"f(x_0) = y_0",[584,1377,1379,1443],{"className":1378,"ariaHidden":666},[665],[584,1380,1382,1385,1388,1391,1431,1434,1437,1440],{"className":1381},[670],[584,1383],{"className":1384,"style":675},[674],[584,1386,605],{"className":1387,"style":681},[679,680],[584,1389,610],{"className":1390},[685],[584,1392,1394,1397],{"className":1393},[679],[584,1395,613],{"className":1396},[679,680],[584,1398,1400],{"className":1399},[724],[584,1401,1403,1423],{"className":1402},[728,1246],[584,1404,1406,1420],{"className":1405},[732],[584,1407,1409],{"className":1408,"style":1253},[736],[584,1410,1411,1414],{"style":1256},[584,1412],{"className":1413,"style":745},[744],[584,1415,1417],{"className":1416},[749,750,751,752],[584,1418,1202],{"className":1419},[679,752],[584,1421,1270],{"className":1422},[1269],[584,1424,1426],{"className":1425},[732],[584,1427,1429],{"className":1428,"style":1277},[736],[584,1430],{},[584,1432,616],{"className":1433},[692],[584,1435],{"className":1436,"style":697},[696],[584,1438,619],{"className":1439},[701],[584,1441],{"className":1442,"style":697},[696],[584,1444,1446,1450],{"className":1445},[670],[584,1447],{"className":1448,"style":1449},[674],"height:0.625em;vertical-align:-0.1944em;",[584,1451,1453,1456],{"className":1452},[679],[584,1454,1210],{"className":1455,"style":1301},[679,680],[584,1457,1459],{"className":1458},[724],[584,1460,1462,1482],{"className":1461},[728,1246],[584,1463,1465,1479],{"className":1464},[732],[584,1466,1468],{"className":1467,"style":1253},[736],[584,1469,1470,1473],{"style":1316},[584,1471],{"className":1472,"style":745},[744],[584,1474,1476],{"className":1475},[749,750,751,752],[584,1477,1202],{"className":1478},[679,752],[584,1480,1270],{"className":1481},[1269],[584,1483,1485],{"className":1484},[732],[584,1486,1488],{"className":1487,"style":1277},[736],[584,1489],{},[577,1491,1492,1493,1567,1568,1709,1710,1713,1714,1862,1863,1033],{},"Extremum bei ",[584,1494,1496,1515],{"className":1495},[587],[584,1497,1499],{"className":1498},[591],[593,1500,1501],{"xmlns":595},[597,1502,1503,1512],{},[600,1504,1505],{},[1196,1506,1507,1509],{},[603,1508,613],{},[603,1510,1511],{},"E",[658,1513,1514],{"encoding":660},"x_E",[584,1516,1518],{"className":1517,"ariaHidden":666},[665],[584,1519,1521,1525],{"className":1520},[670],[584,1522],{"className":1523,"style":1524},[674],"height:0.5806em;vertical-align:-0.15em;",[584,1526,1528,1531],{"className":1527},[679],[584,1529,613],{"className":1530},[679,680],[584,1532,1534],{"className":1533},[724],[584,1535,1537,1559],{"className":1536},[728,1246],[584,1538,1540,1556],{"className":1539},[732],[584,1541,1544],{"className":1542,"style":1543},[736],"height:0.3283em;",[584,1545,1546,1549],{"style":1256},[584,1547],{"className":1548,"style":745},[744],[584,1550,1552],{"className":1551},[749,750,751,752],[584,1553,1511],{"className":1554,"style":1555},[679,680,752],"margin-right:0.0576em;",[584,1557,1270],{"className":1558},[1269],[584,1560,1562],{"className":1561},[732],[584,1563,1565],{"className":1564,"style":1277},[736],[584,1566],{},": ",[584,1569,1571,1603],{"className":1570},[587],[584,1572,1574],{"className":1573},[591],[593,1575,1576],{"xmlns":595},[597,1577,1578,1600],{},[600,1579,1580,1586,1588,1594,1596,1598],{},[624,1581,1582,1584],{},[603,1583,605],{},[607,1585,897],{"mathvariant":895,"lspace":896,"rspace":896},[607,1587,610],{"stretchy":609},[1196,1589,1590,1592],{},[603,1591,613],{},[603,1593,1511],{},[607,1595,616],{"stretchy":609},[607,1597,619],{},[629,1599,1202],{},[658,1601,1602],{"encoding":660},"f'(x_E) = 0",[584,1604,1606,1700],{"className":1605,"ariaHidden":666},[665],[584,1607,1609,1613,1645,1648,1688,1691,1694,1697],{"className":1608},[670],[584,1610],{"className":1611,"style":1612},[674],"height:1.0019em;vertical-align:-0.25em;",[584,1614,1616,1619],{"className":1615},[679],[584,1617,605],{"className":1618,"style":681},[679,680],[584,1620,1622],{"className":1621},[724],[584,1623,1625],{"className":1624},[728],[584,1626,1628],{"className":1627},[732],[584,1629,1631],{"className":1630,"style":929},[736],[584,1632,1633,1636],{"style":740},[584,1634],{"className":1635,"style":745},[744],[584,1637,1639],{"className":1638},[749,750,751,752],[584,1640,1642],{"className":1641},[679,752],[584,1643,897],{"className":1644},[679,752],[584,1646,610],{"className":1647},[685],[584,1649,1651,1654],{"className":1650},[679],[584,1652,613],{"className":1653},[679,680],[584,1655,1657],{"className":1656},[724],[584,1658,1660,1680],{"className":1659},[728,1246],[584,1661,1663,1677],{"className":1662},[732],[584,1664,1666],{"className":1665,"style":1543},[736],[584,1667,1668,1671],{"style":1256},[584,1669],{"className":1670,"style":745},[744],[584,1672,1674],{"className":1673},[749,750,751,752],[584,1675,1511],{"className":1676,"style":1555},[679,680,752],[584,1678,1270],{"className":1679},[1269],[584,1681,1683],{"className":1682},[732],[584,1684,1686],{"className":1685,"style":1277},[736],[584,1687],{},[584,1689,616],{"className":1690},[692],[584,1692],{"className":1693,"style":697},[696],[584,1695,619],{"className":1696},[701],[584,1698],{"className":1699,"style":697},[696],[584,1701,1703,1706],{"className":1702},[670],[584,1704],{"className":1705,"style":872},[674],[584,1707,1202],{"className":1708},[679],". Ein ",[569,1711,1712],{},"Extrempunkt"," ",[584,1715,1717,1749],{"className":1716},[587],[584,1718,1720],{"className":1719},[591],[593,1721,1722],{"xmlns":595},[597,1723,1724,1746],{},[600,1725,1726,1728,1730,1736,1738,1744],{},[603,1727,1511],{},[607,1729,610],{"stretchy":609},[1196,1731,1732,1734],{},[603,1733,613],{},[603,1735,1511],{},[607,1737,1205],{},[1196,1739,1740,1742],{},[603,1741,1210],{},[603,1743,1511],{},[607,1745,616],{"stretchy":609},[658,1747,1748],{"encoding":660},"E(x_E \\mid y_E)",[584,1750,1752,1813],{"className":1751,"ariaHidden":666},[665],[584,1753,1755,1758,1761,1764,1804,1807,1810],{"className":1754},[670],[584,1756],{"className":1757,"style":675},[674],[584,1759,1511],{"className":1760,"style":1555},[679,680],[584,1762,610],{"className":1763},[685],[584,1765,1767,1770],{"className":1766},[679],[584,1768,613],{"className":1769},[679,680],[584,1771,1773],{"className":1772},[724],[584,1774,1776,1796],{"className":1775},[728,1246],[584,1777,1779,1793],{"className":1778},[732],[584,1780,1782],{"className":1781,"style":1543},[736],[584,1783,1784,1787],{"style":1256},[584,1785],{"className":1786,"style":745},[744],[584,1788,1790],{"className":1789},[749,750,751,752],[584,1791,1511],{"className":1792,"style":1555},[679,680,752],[584,1794,1270],{"className":1795},[1269],[584,1797,1799],{"className":1798},[732],[584,1800,1802],{"className":1801,"style":1277},[736],[584,1803],{},[584,1805],{"className":1806,"style":697},[696],[584,1808,1205],{"className":1809},[701],[584,1811],{"className":1812,"style":697},[696],[584,1814,1816,1819,1859],{"className":1815},[670],[584,1817],{"className":1818,"style":675},[674],[584,1820,1822,1825],{"className":1821},[679],[584,1823,1210],{"className":1824,"style":1301},[679,680],[584,1826,1828],{"className":1827},[724],[584,1829,1831,1851],{"className":1830},[728,1246],[584,1832,1834,1848],{"className":1833},[732],[584,1835,1837],{"className":1836,"style":1543},[736],[584,1838,1839,1842],{"style":1316},[584,1840],{"className":1841,"style":745},[744],[584,1843,1845],{"className":1844},[749,750,751,752],[584,1846,1511],{"className":1847,"style":1555},[679,680,752],[584,1849,1270],{"className":1850},[1269],[584,1852,1854],{"className":1853},[732],[584,1855,1857],{"className":1856,"style":1277},[736],[584,1858],{},[584,1860,616],{"className":1861},[692]," liefert zwei Gleichungen: zusätzlich ",[584,1864,1866,1898],{"className":1865},[587],[584,1867,1869],{"className":1868},[591],[593,1870,1871],{"xmlns":595},[597,1872,1873,1895],{},[600,1874,1875,1877,1879,1885,1887,1889],{},[603,1876,605],{},[607,1878,610],{"stretchy":609},[1196,1880,1881,1883],{},[603,1882,613],{},[603,1884,1511],{},[607,1886,616],{"stretchy":609},[607,1888,619],{},[1196,1890,1891,1893],{},[603,1892,1210],{},[603,1894,1511],{},[658,1896,1897],{"encoding":660},"f(x_E) = y_E",[584,1899,1901,1965],{"className":1900,"ariaHidden":666},[665],[584,1902,1904,1907,1910,1913,1953,1956,1959,1962],{"className":1903},[670],[584,1905],{"className":1906,"style":675},[674],[584,1908,605],{"className":1909,"style":681},[679,680],[584,1911,610],{"className":1912},[685],[584,1914,1916,1919],{"className":1915},[679],[584,1917,613],{"className":1918},[679,680],[584,1920,1922],{"className":1921},[724],[584,1923,1925,1945],{"className":1924},[728,1246],[584,1926,1928,1942],{"className":1927},[732],[584,1929,1931],{"className":1930,"style":1543},[736],[584,1932,1933,1936],{"style":1256},[584,1934],{"className":1935,"style":745},[744],[584,1937,1939],{"className":1938},[749,750,751,752],[584,1940,1511],{"className":1941,"style":1555},[679,680,752],[584,1943,1270],{"className":1944},[1269],[584,1946,1948],{"className":1947},[732],[584,1949,1951],{"className":1950,"style":1277},[736],[584,1952],{},[584,1954,616],{"className":1955},[692],[584,1957],{"className":1958,"style":697},[696],[584,1960,619],{"className":1961},[701],[584,1963],{"className":1964,"style":697},[696],[584,1966,1968,1971],{"className":1967},[670],[584,1969],{"className":1970,"style":1449},[674],[584,1972,1974,1977],{"className":1973},[679],[584,1975,1210],{"className":1976,"style":1301},[679,680],[584,1978,1980],{"className":1979},[724],[584,1981,1983,2003],{"className":1982},[728,1246],[584,1984,1986,2000],{"className":1985},[732],[584,1987,1989],{"className":1988,"style":1543},[736],[584,1990,1991,1994],{"style":1316},[584,1992],{"className":1993,"style":745},[744],[584,1995,1997],{"className":1996},[749,750,751,752],[584,1998,1511],{"className":1999,"style":1555},[679,680,752],[584,2001,1270],{"className":2002},[1269],[584,2004,2006],{"className":2005},[732],[584,2007,2009],{"className":2008,"style":1277},[736],[584,2010],{},[577,2012,2013,2014,1567,2085,2229],{},"Wendestelle bei ",[584,2015,2017,2036],{"className":2016},[587],[584,2018,2020],{"className":2019},[591],[593,2021,2022],{"xmlns":595},[597,2023,2024,2033],{},[600,2025,2026],{},[1196,2027,2028,2030],{},[603,2029,613],{},[603,2031,2032],{},"W",[658,2034,2035],{"encoding":660},"x_W",[584,2037,2039],{"className":2038,"ariaHidden":666},[665],[584,2040,2042,2045],{"className":2041},[670],[584,2043],{"className":2044,"style":1524},[674],[584,2046,2048,2051],{"className":2047},[679],[584,2049,613],{"className":2050},[679,680],[584,2052,2054],{"className":2053},[724],[584,2055,2057,2077],{"className":2056},[728,1246],[584,2058,2060,2074],{"className":2059},[732],[584,2061,2063],{"className":2062,"style":1543},[736],[584,2064,2065,2068],{"style":1256},[584,2066],{"className":2067,"style":745},[744],[584,2069,2071],{"className":2070},[749,750,751,752],[584,2072,2032],{"className":2073,"style":1230},[679,680,752],[584,2075,1270],{"className":2076},[1269],[584,2078,2080],{"className":2079},[732],[584,2081,2083],{"className":2082,"style":1277},[736],[584,2084],{},[584,2086,2088,2124],{"className":2087},[587],[584,2089,2091],{"className":2090},[591],[593,2092,2093],{"xmlns":595},[597,2094,2095,2121],{},[600,2096,2097,2107,2109,2115,2117,2119],{},[624,2098,2099,2101],{},[603,2100,605],{},[600,2102,2103,2105],{},[607,2104,897],{"mathvariant":895},[607,2106,897],{"mathvariant":895},[607,2108,610],{"stretchy":609},[1196,2110,2111,2113],{},[603,2112,613],{},[603,2114,2032],{},[607,2116,616],{"stretchy":609},[607,2118,619],{},[629,2120,1202],{},[658,2122,2123],{"encoding":660},"f''(x_W) = 0",[584,2125,2127,2220],{"className":2126,"ariaHidden":666},[665],[584,2128,2130,2133,2165,2168,2208,2211,2214,2217],{"className":2129},[670],[584,2131],{"className":2132,"style":1612},[674],[584,2134,2136,2139],{"className":2135},[679],[584,2137,605],{"className":2138,"style":681},[679,680],[584,2140,2142],{"className":2141},[724],[584,2143,2145],{"className":2144},[728],[584,2146,2148],{"className":2147},[732],[584,2149,2151],{"className":2150,"style":929},[736],[584,2152,2153,2156],{"style":740},[584,2154],{"className":2155,"style":745},[744],[584,2157,2159],{"className":2158},[749,750,751,752],[584,2160,2162],{"className":2161},[679,752],[584,2163,1011],{"className":2164},[679,752],[584,2166,610],{"className":2167},[685],[584,2169,2171,2174],{"className":2170},[679],[584,2172,613],{"className":2173},[679,680],[584,2175,2177],{"className":2176},[724],[584,2178,2180,2200],{"className":2179},[728,1246],[584,2181,2183,2197],{"className":2182},[732],[584,2184,2186],{"className":2185,"style":1543},[736],[584,2187,2188,2191],{"style":1256},[584,2189],{"className":2190,"style":745},[744],[584,2192,2194],{"className":2193},[749,750,751,752],[584,2195,2032],{"className":2196,"style":1230},[679,680,752],[584,2198,1270],{"className":2199},[1269],[584,2201,2203],{"className":2202},[732],[584,2204,2206],{"className":2205,"style":1277},[736],[584,2207],{},[584,2209,616],{"className":2210},[692],[584,2212],{"className":2213,"style":697},[696],[584,2215,619],{"className":2216},[701],[584,2218],{"className":2219,"style":697},[696],[584,2221,2223,2226],{"className":2222},[670],[584,2224],{"className":2225,"style":872},[674],[584,2227,1202],{"className":2228},[679],". Ein Wendepunkt liefert ebenfalls zwei Gleichungen.",[577,2231,2232,2233,2262,2263,2333,2334,1033],{},"Steigung ",[584,2234,2236,2250],{"className":2235},[587],[584,2237,2239],{"className":2238},[591],[593,2240,2241],{"xmlns":595},[597,2242,2243,2248],{},[600,2244,2245],{},[603,2246,2247],{},"m",[658,2249,2247],{"encoding":660},[584,2251,2253],{"className":2252,"ariaHidden":666},[665],[584,2254,2256,2259],{"className":2255},[670],[584,2257],{"className":2258,"style":1063},[674],[584,2260,2247],{"className":2261},[679,680]," an der Stelle ",[584,2264,2266,2284],{"className":2265},[587],[584,2267,2269],{"className":2268},[591],[593,2270,2271],{"xmlns":595},[597,2272,2273,2281],{},[600,2274,2275],{},[1196,2276,2277,2279],{},[603,2278,613],{},[629,2280,1202],{},[658,2282,2283],{"encoding":660},"x_0",[584,2285,2287],{"className":2286,"ariaHidden":666},[665],[584,2288,2290,2293],{"className":2289},[670],[584,2291],{"className":2292,"style":1524},[674],[584,2294,2296,2299],{"className":2295},[679],[584,2297,613],{"className":2298},[679,680],[584,2300,2302],{"className":2301},[724],[584,2303,2305,2325],{"className":2304},[728,1246],[584,2306,2308,2322],{"className":2307},[732],[584,2309,2311],{"className":2310,"style":1253},[736],[584,2312,2313,2316],{"style":1256},[584,2314],{"className":2315,"style":745},[744],[584,2317,2319],{"className":2318},[749,750,751,752],[584,2320,1202],{"className":2321},[679,752],[584,2323,1270],{"className":2324},[1269],[584,2326,2328],{"className":2327},[732],[584,2329,2331],{"className":2330,"style":1277},[736],[584,2332],{},", z.B. aus einer Tangente: ",[584,2335,2337,2369],{"className":2336},[587],[584,2338,2340],{"className":2339},[591],[593,2341,2342],{"xmlns":595},[597,2343,2344,2366],{},[600,2345,2346,2352,2354,2360,2362,2364],{},[624,2347,2348,2350],{},[603,2349,605],{},[607,2351,897],{"mathvariant":895,"lspace":896,"rspace":896},[607,2353,610],{"stretchy":609},[1196,2355,2356,2358],{},[603,2357,613],{},[629,2359,1202],{},[607,2361,616],{"stretchy":609},[607,2363,619],{},[603,2365,2247],{},[658,2367,2368],{"encoding":660},"f'(x_0) = m",[584,2370,2372,2465],{"className":2371,"ariaHidden":666},[665],[584,2373,2375,2378,2410,2413,2453,2456,2459,2462],{"className":2374},[670],[584,2376],{"className":2377,"style":1612},[674],[584,2379,2381,2384],{"className":2380},[679],[584,2382,605],{"className":2383,"style":681},[679,680],[584,2385,2387],{"className":2386},[724],[584,2388,2390],{"className":2389},[728],[584,2391,2393],{"className":2392},[732],[584,2394,2396],{"className":2395,"style":929},[736],[584,2397,2398,2401],{"style":740},[584,2399],{"className":2400,"style":745},[744],[584,2402,2404],{"className":2403},[749,750,751,752],[584,2405,2407],{"className":2406},[679,752],[584,2408,897],{"className":2409},[679,752],[584,2411,610],{"className":2412},[685],[584,2414,2416,2419],{"className":2415},[679],[584,2417,613],{"className":2418},[679,680],[584,2420,2422],{"className":2421},[724],[584,2423,2425,2445],{"className":2424},[728,1246],[584,2426,2428,2442],{"className":2427},[732],[584,2429,2431],{"className":2430,"style":1253},[736],[584,2432,2433,2436],{"style":1256},[584,2434],{"className":2435,"style":745},[744],[584,2437,2439],{"className":2438},[749,750,751,752],[584,2440,1202],{"className":2441},[679,752],[584,2443,1270],{"className":2444},[1269],[584,2446,2448],{"className":2447},[732],[584,2449,2451],{"className":2450,"style":1277},[736],[584,2452],{},[584,2454,616],{"className":2455},[692],[584,2457],{"className":2458,"style":697},[696],[584,2460,619],{"className":2461},[701],[584,2463],{"className":2464,"style":697},[696],[584,2466,2468,2471],{"className":2467},[670],[584,2469],{"className":2470,"style":1063},[674],[584,2472,2247],{"className":2473},[679,680],[577,2475,2476],{},"Achsensymmetrie zur y-Achse: nur gerade Exponenten. Punktsymmetrie zum Ursprung: nur ungerade Exponenten. Das verringert die Zahl der Unbekannten.",[560,2478,2480],{"id":2479},"beispiele","Beispiele",[565,2482,2483,2484,2545,2546,2597,2598,2665,2666,2860,2861,3003],{},"Gesucht ist eine Funktion 3. Grades mit Extremum im Punkt ",[584,2485,2487,2509],{"className":2486},[587],[584,2488,2490],{"className":2489},[591],[593,2491,2492],{"xmlns":595},[597,2493,2494,2506],{},[600,2495,2496,2498,2500,2502,2504],{},[607,2497,610],{"stretchy":609},[629,2499,1202],{},[607,2501,1205],{},[629,2503,1086],{},[607,2505,616],{"stretchy":609},[658,2507,2508],{"encoding":660},"(0 \\mid 1)",[584,2510,2512,2533],{"className":2511,"ariaHidden":666},[665],[584,2513,2515,2518,2521,2524,2527,2530],{"className":2514},[670],[584,2516],{"className":2517,"style":675},[674],[584,2519,610],{"className":2520},[685],[584,2522,1202],{"className":2523},[679],[584,2525],{"className":2526,"style":697},[696],[584,2528,1205],{"className":2529},[701],[584,2531],{"className":2532,"style":697},[696],[584,2534,2536,2539,2542],{"className":2535},[670],[584,2537],{"className":2538,"style":675},[674],[584,2540,1086],{"className":2541},[679],[584,2543,616],{"className":2544},[692],", einer Wendestelle bei ",[584,2547,2549,2567],{"className":2548},[587],[584,2550,2552],{"className":2551},[591],[593,2553,2554],{"xmlns":595},[597,2555,2556,2564],{},[600,2557,2558,2560,2562],{},[603,2559,613],{},[607,2561,619],{},[629,2563,1086],{},[658,2565,2566],{"encoding":660},"x = 1",[584,2568,2570,2588],{"className":2569,"ariaHidden":666},[665],[584,2571,2573,2576,2579,2582,2585],{"className":2572},[670],[584,2574],{"className":2575,"style":1063},[674],[584,2577,613],{"className":2578},[679,680],[584,2580],{"className":2581,"style":697},[696],[584,2583,619],{"className":2584},[701],[584,2586],{"className":2587,"style":697},[696],[584,2589,2591,2594],{"className":2590},[670],[584,2592],{"className":2593,"style":872},[674],[584,2595,1086],{"className":2596},[679],", die durch ",[584,2599,2601,2626],{"className":2600},[587],[584,2602,2604],{"className":2603},[591],[593,2605,2606],{"xmlns":595},[597,2607,2608,2623],{},[600,2609,2610,2612,2614,2616,2619,2621],{},[607,2611,610],{"stretchy":609},[629,2613,644],{},[607,2615,1205],{},[607,2617,2618],{},"−",[629,2620,631],{},[607,2622,616],{"stretchy":609},[658,2624,2625],{"encoding":660},"(2 \\mid -3)",[584,2627,2629,2650],{"className":2628,"ariaHidden":666},[665],[584,2630,2632,2635,2638,2641,2644,2647],{"className":2631},[670],[584,2633],{"className":2634,"style":675},[674],[584,2636,610],{"className":2637},[685],[584,2639,644],{"className":2640},[679],[584,2642],{"className":2643,"style":697},[696],[584,2645,1205],{"className":2646},[701],[584,2648],{"className":2649,"style":697},[696],[584,2651,2653,2656,2659,2662],{"className":2652},[670],[584,2654],{"className":2655,"style":675},[674],[584,2657,2618],{"className":2658},[679],[584,2660,631],{"className":2661},[679],[584,2663,616],{"className":2664},[692]," verläuft. Mit ",[584,2667,2669,2717],{"className":2668},[587],[584,2670,2672],{"className":2671},[591],[593,2673,2674],{"xmlns":595},[597,2675,2676,2714],{},[600,2677,2678,2684,2686,2688,2690,2692,2694,2696,2702,2704,2706,2708,2710,2712],{},[624,2679,2680,2682],{},[603,2681,605],{},[607,2683,897],{"mathvariant":895,"lspace":896,"rspace":896},[607,2685,610],{"stretchy":609},[603,2687,613],{},[607,2689,616],{"stretchy":609},[607,2691,619],{},[629,2693,631],{},[603,2695,622],{},[624,2697,2698,2700],{},[603,2699,613],{},[629,2701,644],{},[607,2703,634],{},[629,2705,644],{},[603,2707,637],{},[603,2709,613],{},[607,2711,634],{},[603,2713,649],{},[658,2715,2716],{"encoding":660},"f'(x) = 3ax^2 + 2bx + c",[584,2718,2720,2776,2826,2851],{"className":2719,"ariaHidden":666},[665],[584,2721,2723,2726,2758,2761,2764,2767,2770,2773],{"className":2722},[670],[584,2724],{"className":2725,"style":1612},[674],[584,2727,2729,2732],{"className":2728},[679],[584,2730,605],{"className":2731,"style":681},[679,680],[584,2733,2735],{"className":2734},[724],[584,2736,2738],{"className":2737},[728],[584,2739,2741],{"className":2740},[732],[584,2742,2744],{"className":2743,"style":929},[736],[584,2745,2746,2749],{"style":740},[584,2747],{"className":2748,"style":745},[744],[584,2750,2752],{"className":2751},[749,750,751,752],[584,2753,2755],{"className":2754},[679,752],[584,2756,897],{"className":2757},[679,752],[584,2759,610],{"className":2760},[685],[584,2762,613],{"className":2763},[679,680],[584,2765,616],{"className":2766},[692],[584,2768],{"className":2769,"style":697},[696],[584,2771,619],{"className":2772},[701],[584,2774],{"className":2775,"style":697},[696],[584,2777,2779,2782,2785,2788,2817,2820,2823],{"className":2778},[670],[584,2780],{"className":2781,"style":711},[674],[584,2783,631],{"className":2784},[679],[584,2786,622],{"className":2787},[679,680],[584,2789,2791,2794],{"className":2790},[679],[584,2792,613],{"className":2793},[679,680],[584,2795,2797],{"className":2796},[724],[584,2798,2800],{"className":2799},[728],[584,2801,2803],{"className":2802},[732],[584,2804,2806],{"className":2805,"style":737},[736],[584,2807,2808,2811],{"style":740},[584,2809],{"className":2810,"style":745},[744],[584,2812,2814],{"className":2813},[749,750,751,752],[584,2815,644],{"className":2816},[679,752],[584,2818],{"className":2819,"style":759},[696],[584,2821,634],{"className":2822},[763],[584,2824],{"className":2825,"style":759},[696],[584,2827,2829,2833,2836,2839,2842,2845,2848],{"className":2828},[670],[584,2830],{"className":2831,"style":2832},[674],"height:0.7778em;vertical-align:-0.0833em;",[584,2834,644],{"className":2835},[679],[584,2837,637],{"className":2838},[679,680],[584,2840,613],{"className":2841},[679,680],[584,2843],{"className":2844,"style":759},[696],[584,2846,634],{"className":2847},[763],[584,2849],{"className":2850,"style":759},[696],[584,2852,2854,2857],{"className":2853},[670],[584,2855],{"className":2856,"style":1063},[674],[584,2858,649],{"className":2859},[679,680]," und ",[584,2862,2864,2907],{"className":2863},[587],[584,2865,2867],{"className":2866},[591],[593,2868,2869],{"xmlns":595},[597,2870,2871,2904],{},[600,2872,2873,2883,2885,2887,2889,2891,2894,2896,2898,2900,2902],{},[624,2874,2875,2877],{},[603,2876,605],{},[600,2878,2879,2881],{},[607,2880,897],{"mathvariant":895},[607,2882,897],{"mathvariant":895},[607,2884,610],{"stretchy":609},[603,2886,613],{},[607,2888,616],{"stretchy":609},[607,2890,619],{},[629,2892,2893],{},"6",[603,2895,622],{},[603,2897,613],{},[607,2899,634],{},[629,2901,644],{},[603,2903,637],{},[658,2905,2906],{"encoding":660},"f''(x) = 6ax + 2b",[584,2908,2910,2966,2991],{"className":2909,"ariaHidden":666},[665],[584,2911,2913,2916,2948,2951,2954,2957,2960,2963],{"className":2912},[670],[584,2914],{"className":2915,"style":1612},[674],[584,2917,2919,2922],{"className":2918},[679],[584,2920,605],{"className":2921,"style":681},[679,680],[584,2923,2925],{"className":2924},[724],[584,2926,2928],{"className":2927},[728],[584,2929,2931],{"className":2930},[732],[584,2932,2934],{"className":2933,"style":929},[736],[584,2935,2936,2939],{"style":740},[584,2937],{"className":2938,"style":745},[744],[584,2940,2942],{"className":2941},[749,750,751,752],[584,2943,2945],{"className":2944},[679,752],[584,2946,1011],{"className":2947},[679,752],[584,2949,610],{"className":2950},[685],[584,2952,613],{"className":2953},[679,680],[584,2955,616],{"className":2956},[692],[584,2958],{"className":2959,"style":697},[696],[584,2961,619],{"className":2962},[701],[584,2964],{"className":2965,"style":697},[696],[584,2967,2969,2973,2976,2979,2982,2985,2988],{"className":2968},[670],[584,2970],{"className":2971,"style":2972},[674],"height:0.7278em;vertical-align:-0.0833em;",[584,2974,2893],{"className":2975},[679],[584,2977,622],{"className":2978},[679,680],[584,2980,613],{"className":2981},[679,680],[584,2983],{"className":2984,"style":759},[696],[584,2986,634],{"className":2987},[763],[584,2989],{"className":2990,"style":759},[696],[584,2992,2994,2997,3000],{"className":2993},[670],[584,2995],{"className":2996,"style":842},[674],[584,2998,644],{"className":2999},[679],[584,3001,637],{"className":3002},[679,680],":",[1173,3005,3006,3125,3277,3527],{},[577,3007,3008,1567,3074],{},[584,3009,3011,3035],{"className":3010},[587],[584,3012,3014],{"className":3013},[591],[593,3015,3016],{"xmlns":595},[597,3017,3018,3032],{},[600,3019,3020,3022,3024,3026,3028,3030],{},[603,3021,605],{},[607,3023,610],{"stretchy":609},[629,3025,1202],{},[607,3027,616],{"stretchy":609},[607,3029,619],{},[629,3031,1086],{},[658,3033,3034],{"encoding":660},"f(0) = 1",[584,3036,3038,3065],{"className":3037,"ariaHidden":666},[665],[584,3039,3041,3044,3047,3050,3053,3056,3059,3062],{"className":3040},[670],[584,3042],{"className":3043,"style":675},[674],[584,3045,605],{"className":3046,"style":681},[679,680],[584,3048,610],{"className":3049},[685],[584,3051,1202],{"className":3052},[679],[584,3054,616],{"className":3055},[692],[584,3057],{"className":3058,"style":697},[696],[584,3060,619],{"className":3061},[701],[584,3063],{"className":3064,"style":697},[696],[584,3066,3068,3071],{"className":3067},[670],[584,3069],{"className":3070,"style":872},[674],[584,3072,1086],{"className":3073},[679],[584,3075,3077,3095],{"className":3076},[587],[584,3078,3080],{"className":3079},[591],[593,3081,3082],{"xmlns":595},[597,3083,3084,3092],{},[600,3085,3086,3088,3090],{},[603,3087,656],{},[607,3089,619],{},[629,3091,1086],{},[658,3093,3094],{"encoding":660},"d = 1",[584,3096,3098,3116],{"className":3097,"ariaHidden":666},[665],[584,3099,3101,3104,3107,3110,3113],{"className":3100},[670],[584,3102],{"className":3103,"style":842},[674],[584,3105,656],{"className":3106},[679,680],[584,3108],{"className":3109,"style":697},[696],[584,3111,619],{"className":3112},[701],[584,3114],{"className":3115,"style":697},[696],[584,3117,3119,3122],{"className":3118},[670],[584,3120],{"className":3121,"style":872},[674],[584,3123,1086],{"className":3124},[679],[577,3126,3127,1567,3226],{},[584,3128,3130,3158],{"className":3129},[587],[584,3131,3133],{"className":3132},[591],[593,3134,3135],{"xmlns":595},[597,3136,3137,3155],{},[600,3138,3139,3145,3147,3149,3151,3153],{},[624,3140,3141,3143],{},[603,3142,605],{},[607,3144,897],{"mathvariant":895,"lspace":896,"rspace":896},[607,3146,610],{"stretchy":609},[629,3148,1202],{},[607,3150,616],{"stretchy":609},[607,3152,619],{},[629,3154,1202],{},[658,3156,3157],{"encoding":660},"f'(0) = 0",[584,3159,3161,3217],{"className":3160,"ariaHidden":666},[665],[584,3162,3164,3167,3199,3202,3205,3208,3211,3214],{"className":3163},[670],[584,3165],{"className":3166,"style":1612},[674],[584,3168,3170,3173],{"className":3169},[679],[584,3171,605],{"className":3172,"style":681},[679,680],[584,3174,3176],{"className":3175},[724],[584,3177,3179],{"className":3178},[728],[584,3180,3182],{"className":3181},[732],[584,3183,3185],{"className":3184,"style":929},[736],[584,3186,3187,3190],{"style":740},[584,3188],{"className":3189,"style":745},[744],[584,3191,3193],{"className":3192},[749,750,751,752],[584,3194,3196],{"className":3195},[679,752],[584,3197,897],{"className":3198},[679,752],[584,3200,610],{"className":3201},[685],[584,3203,1202],{"className":3204},[679],[584,3206,616],{"className":3207},[692],[584,3209],{"className":3210,"style":697},[696],[584,3212,619],{"className":3213},[701],[584,3215],{"className":3216,"style":697},[696],[584,3218,3220,3223],{"className":3219},[670],[584,3221],{"className":3222,"style":872},[674],[584,3224,1202],{"className":3225},[679],[584,3227,3229,3247],{"className":3228},[587],[584,3230,3232],{"className":3231},[591],[593,3233,3234],{"xmlns":595},[597,3235,3236,3244],{},[600,3237,3238,3240,3242],{},[603,3239,649],{},[607,3241,619],{},[629,3243,1202],{},[658,3245,3246],{"encoding":660},"c = 0",[584,3248,3250,3268],{"className":3249,"ariaHidden":666},[665],[584,3251,3253,3256,3259,3262,3265],{"className":3252},[670],[584,3254],{"className":3255,"style":1063},[674],[584,3257,649],{"className":3258},[679,680],[584,3260],{"className":3261,"style":697},[696],[584,3263,619],{"className":3264},[701],[584,3266],{"className":3267,"style":697},[696],[584,3269,3271,3274],{"className":3270},[670],[584,3272],{"className":3273,"style":872},[674],[584,3275,1202],{"className":3276},[679],[577,3278,3279,1567,3382,3465,3466],{},[584,3280,3282,3314],{"className":3281},[587],[584,3283,3285],{"className":3284},[591],[593,3286,3287],{"xmlns":595},[597,3288,3289,3311],{},[600,3290,3291,3301,3303,3305,3307,3309],{},[624,3292,3293,3295],{},[603,3294,605],{},[600,3296,3297,3299],{},[607,3298,897],{"mathvariant":895},[607,3300,897],{"mathvariant":895},[607,3302,610],{"stretchy":609},[629,3304,1086],{},[607,3306,616],{"stretchy":609},[607,3308,619],{},[629,3310,1202],{},[658,3312,3313],{"encoding":660},"f''(1) = 0",[584,3315,3317,3373],{"className":3316,"ariaHidden":666},[665],[584,3318,3320,3323,3355,3358,3361,3364,3367,3370],{"className":3319},[670],[584,3321],{"className":3322,"style":1612},[674],[584,3324,3326,3329],{"className":3325},[679],[584,3327,605],{"className":3328,"style":681},[679,680],[584,3330,3332],{"className":3331},[724],[584,3333,3335],{"className":3334},[728],[584,3336,3338],{"className":3337},[732],[584,3339,3341],{"className":3340,"style":929},[736],[584,3342,3343,3346],{"style":740},[584,3344],{"className":3345,"style":745},[744],[584,3347,3349],{"className":3348},[749,750,751,752],[584,3350,3352],{"className":3351},[679,752],[584,3353,1011],{"className":3354},[679,752],[584,3356,610],{"className":3357},[685],[584,3359,1086],{"className":3360},[679],[584,3362,616],{"className":3363},[692],[584,3365],{"className":3366,"style":697},[696],[584,3368,619],{"className":3369},[701],[584,3371],{"className":3372,"style":697},[696],[584,3374,3376,3379],{"className":3375},[670],[584,3377],{"className":3378,"style":872},[674],[584,3380,1202],{"className":3381},[679],[584,3383,3385,3411],{"className":3384},[587],[584,3386,3388],{"className":3387},[591],[593,3389,3390],{"xmlns":595},[597,3391,3392,3408],{},[600,3393,3394,3396,3398,3400,3402,3404,3406],{},[629,3395,2893],{},[603,3397,622],{},[607,3399,634],{},[629,3401,644],{},[603,3403,637],{},[607,3405,619],{},[629,3407,1202],{},[658,3409,3410],{"encoding":660},"6a + 2b = 0",[584,3412,3414,3435,3456],{"className":3413,"ariaHidden":666},[665],[584,3415,3417,3420,3423,3426,3429,3432],{"className":3416},[670],[584,3418],{"className":3419,"style":2972},[674],[584,3421,2893],{"className":3422},[679],[584,3424,622],{"className":3425},[679,680],[584,3427],{"className":3428,"style":759},[696],[584,3430,634],{"className":3431},[763],[584,3433],{"className":3434,"style":759},[696],[584,3436,3438,3441,3444,3447,3450,3453],{"className":3437},[670],[584,3439],{"className":3440,"style":842},[674],[584,3442,644],{"className":3443},[679],[584,3445,637],{"className":3446},[679,680],[584,3448],{"className":3449,"style":697},[696],[584,3451,619],{"className":3452},[701],[584,3454],{"className":3455,"style":697},[696],[584,3457,3459,3462],{"className":3458},[670],[584,3460],{"className":3461,"style":872},[674],[584,3463,1202],{"className":3464},[679],", also ",[584,3467,3469,3491],{"className":3468},[587],[584,3470,3472],{"className":3471},[591],[593,3473,3474],{"xmlns":595},[597,3475,3476,3488],{},[600,3477,3478,3480,3482,3484,3486],{},[603,3479,637],{},[607,3481,619],{},[607,3483,2618],{},[629,3485,631],{},[603,3487,622],{},[658,3489,3490],{"encoding":660},"b = -3a",[584,3492,3494,3512],{"className":3493,"ariaHidden":666},[665],[584,3495,3497,3500,3503,3506,3509],{"className":3496},[670],[584,3498],{"className":3499,"style":842},[674],[584,3501,637],{"className":3502},[679,680],[584,3504],{"className":3505,"style":697},[696],[584,3507,619],{"className":3508},[701],[584,3510],{"className":3511,"style":697},[696],[584,3513,3515,3518,3521,3524],{"className":3514},[670],[584,3516],{"className":3517,"style":2972},[674],[584,3519,2618],{"className":3520},[679],[584,3522,631],{"className":3523},[679],[584,3525,622],{"className":3526},[679,680],[577,3528,3529,1567,3600],{},[584,3530,3532,3558],{"className":3531},[587],[584,3533,3535],{"className":3534},[591],[593,3536,3537],{"xmlns":595},[597,3538,3539,3555],{},[600,3540,3541,3543,3545,3547,3549,3551,3553],{},[603,3542,605],{},[607,3544,610],{"stretchy":609},[629,3546,644],{},[607,3548,616],{"stretchy":609},[607,3550,619],{},[607,3552,2618],{},[629,3554,631],{},[658,3556,3557],{"encoding":660},"f(2) = -3",[584,3559,3561,3588],{"className":3560,"ariaHidden":666},[665],[584,3562,3564,3567,3570,3573,3576,3579,3582,3585],{"className":3563},[670],[584,3565],{"className":3566,"style":675},[674],[584,3568,605],{"className":3569,"style":681},[679,680],[584,3571,610],{"className":3572},[685],[584,3574,644],{"className":3575},[679],[584,3577,616],{"className":3578},[692],[584,3580],{"className":3581,"style":697},[696],[584,3583,619],{"className":3584},[701],[584,3586],{"className":3587,"style":697},[696],[584,3589,3591,3594,3597],{"className":3590},[670],[584,3592],{"className":3593,"style":2972},[674],[584,3595,2618],{"className":3596},[679],[584,3598,631],{"className":3599},[679],[584,3601,3603,3643],{"className":3602},[587],[584,3604,3606],{"className":3605},[591],[593,3607,3608],{"xmlns":595},[597,3609,3610,3640],{},[600,3611,3612,3615,3617,3619,3622,3624,3626,3628,3630,3632,3634,3636,3638],{},[629,3613,3614],{},"8",[603,3616,622],{},[607,3618,634],{},[629,3620,3621],{},"4",[603,3623,637],{},[607,3625,634],{},[629,3627,644],{},[603,3629,649],{},[607,3631,634],{},[603,3633,656],{},[607,3635,619],{},[607,3637,2618],{},[629,3639,631],{},[658,3641,3642],{"encoding":660},"8a + 4b + 2c + d = -3",[584,3644,3646,3667,3688,3709,3727],{"className":3645,"ariaHidden":666},[665],[584,3647,3649,3652,3655,3658,3661,3664],{"className":3648},[670],[584,3650],{"className":3651,"style":2972},[674],[584,3653,3614],{"className":3654},[679],[584,3656,622],{"className":3657},[679,680],[584,3659],{"className":3660,"style":759},[696],[584,3662,634],{"className":3663},[763],[584,3665],{"className":3666,"style":759},[696],[584,3668,3670,3673,3676,3679,3682,3685],{"className":3669},[670],[584,3671],{"className":3672,"style":2832},[674],[584,3674,3621],{"className":3675},[679],[584,3677,637],{"className":3678},[679,680],[584,3680],{"className":3681,"style":759},[696],[584,3683,634],{"className":3684},[763],[584,3686],{"className":3687,"style":759},[696],[584,3689,3691,3694,3697,3700,3703,3706],{"className":3690},[670],[584,3692],{"className":3693,"style":2972},[674],[584,3695,644],{"className":3696},[679],[584,3698,649],{"className":3699},[679,680],[584,3701],{"className":3702,"style":759},[696],[584,3704,634],{"className":3705},[763],[584,3707],{"className":3708,"style":759},[696],[584,3710,3712,3715,3718,3721,3724],{"className":3711},[670],[584,3713],{"className":3714,"style":842},[674],[584,3716,656],{"className":3717},[679,680],[584,3719],{"className":3720,"style":697},[696],[584,3722,619],{"className":3723},[701],[584,3725],{"className":3726,"style":697},[696],[584,3728,3730,3733,3736],{"className":3729},[670],[584,3731],{"className":3732,"style":2972},[674],[584,3734,2618],{"className":3735},[679],[584,3737,631],{"className":3738},[679],[565,3740,3741,3742,3465,3853,2860,3904,3003],{},"Einsetzen in die letzte Gleichung: ",[584,3743,3745,3778],{"className":3744},[587],[584,3746,3748],{"className":3747},[591],[593,3749,3750],{"xmlns":595},[597,3751,3752,3775],{},[600,3753,3754,3756,3758,3760,3763,3765,3767,3769,3771,3773],{},[629,3755,3614],{},[603,3757,622],{},[607,3759,2618],{},[629,3761,3762],{},"12",[603,3764,622],{},[607,3766,634],{},[629,3768,1086],{},[607,3770,619],{},[607,3772,2618],{},[629,3774,631],{},[658,3776,3777],{"encoding":660},"8a - 12a + 1 = -3",[584,3779,3781,3802,3823,3841],{"className":3780,"ariaHidden":666},[665],[584,3782,3784,3787,3790,3793,3796,3799],{"className":3783},[670],[584,3785],{"className":3786,"style":2972},[674],[584,3788,3614],{"className":3789},[679],[584,3791,622],{"className":3792},[679,680],[584,3794],{"className":3795,"style":759},[696],[584,3797,2618],{"className":3798},[763],[584,3800],{"className":3801,"style":759},[696],[584,3803,3805,3808,3811,3814,3817,3820],{"className":3804},[670],[584,3806],{"className":3807,"style":2972},[674],[584,3809,3762],{"className":3810},[679],[584,3812,622],{"className":3813},[679,680],[584,3815],{"className":3816,"style":759},[696],[584,3818,634],{"className":3819},[763],[584,3821],{"className":3822,"style":759},[696],[584,3824,3826,3829,3832,3835,3838],{"className":3825},[670],[584,3827],{"className":3828,"style":872},[674],[584,3830,1086],{"className":3831},[679],[584,3833],{"className":3834,"style":697},[696],[584,3836,619],{"className":3837},[701],[584,3839],{"className":3840,"style":697},[696],[584,3842,3844,3847,3850],{"className":3843},[670],[584,3845],{"className":3846,"style":2972},[674],[584,3848,2618],{"className":3849},[679],[584,3851,631],{"className":3852},[679],[584,3854,3856,3874],{"className":3855},[587],[584,3857,3859],{"className":3858},[591],[593,3860,3861],{"xmlns":595},[597,3862,3863,3871],{},[600,3864,3865,3867,3869],{},[603,3866,622],{},[607,3868,619],{},[629,3870,1086],{},[658,3872,3873],{"encoding":660},"a = 1",[584,3875,3877,3895],{"className":3876,"ariaHidden":666},[665],[584,3878,3880,3883,3886,3889,3892],{"className":3879},[670],[584,3881],{"className":3882,"style":1063},[674],[584,3884,622],{"className":3885},[679,680],[584,3887],{"className":3888,"style":697},[696],[584,3890,619],{"className":3891},[701],[584,3893],{"className":3894,"style":697},[696],[584,3896,3898,3901],{"className":3897},[670],[584,3899],{"className":3900,"style":872},[674],[584,3902,1086],{"className":3903},[679],[584,3905,3907,3927],{"className":3906},[587],[584,3908,3910],{"className":3909},[591],[593,3911,3912],{"xmlns":595},[597,3913,3914,3924],{},[600,3915,3916,3918,3920,3922],{},[603,3917,637],{},[607,3919,619],{},[607,3921,2618],{},[629,3923,631],{},[658,3925,3926],{"encoding":660},"b = -3",[584,3928,3930,3948],{"className":3929,"ariaHidden":666},[665],[584,3931,3933,3936,3939,3942,3945],{"className":3932},[670],[584,3934],{"className":3935,"style":842},[674],[584,3937,637],{"className":3938},[679,680],[584,3940],{"className":3941,"style":697},[696],[584,3943,619],{"className":3944},[701],[584,3946],{"className":3947,"style":697},[696],[584,3949,3951,3954,3957],{"className":3950},[670],[584,3952],{"className":3953,"style":2972},[674],[584,3955,2618],{"className":3956},[679],[584,3958,631],{"className":3959},[679],[584,3961,3964],{"className":3962},[3963],"katex-display",[584,3965,3967,4010],{"className":3966},[587],[584,3968,3970],{"className":3969},[591],[593,3971,3973],{"xmlns":595,"display":3972},"block",[597,3974,3975,4007],{},[600,3976,3977,3979,3981,3983,3985,3987,3993,3995,3997,4003,4005],{},[603,3978,605],{},[607,3980,610],{"stretchy":609},[603,3982,613],{},[607,3984,616],{"stretchy":609},[607,3986,619],{},[624,3988,3989,3991],{},[603,3990,613],{},[629,3992,631],{},[607,3994,2618],{},[629,3996,631],{},[624,3998,3999,4001],{},[603,4000,613],{},[629,4002,644],{},[607,4004,634],{},[629,4006,1086],{},[658,4008,4009],{"encoding":660},"f(x) = x^3 - 3x^2 + 1",[584,4011,4013,4040,4087,4134],{"className":4012,"ariaHidden":666},[665],[584,4014,4016,4019,4022,4025,4028,4031,4034,4037],{"className":4015},[670],[584,4017],{"className":4018,"style":675},[674],[584,4020,605],{"className":4021,"style":681},[679,680],[584,4023,610],{"className":4024},[685],[584,4026,613],{"className":4027},[679,680],[584,4029,616],{"className":4030},[692],[584,4032],{"className":4033,"style":697},[696],[584,4035,619],{"className":4036},[701],[584,4038],{"className":4039,"style":697},[696],[584,4041,4043,4047,4078,4081,4084],{"className":4042},[670],[584,4044],{"className":4045,"style":4046},[674],"height:0.9474em;vertical-align:-0.0833em;",[584,4048,4050,4053],{"className":4049},[679],[584,4051,613],{"className":4052},[679,680],[584,4054,4056],{"className":4055},[724],[584,4057,4059],{"className":4058},[728],[584,4060,4062],{"className":4061},[732],[584,4063,4066],{"className":4064,"style":4065},[736],"height:0.8641em;",[584,4067,4069,4072],{"style":4068},"top:-3.113em;margin-right:0.05em;",[584,4070],{"className":4071,"style":745},[744],[584,4073,4075],{"className":4074},[749,750,751,752],[584,4076,631],{"className":4077},[679,752],[584,4079],{"className":4080,"style":759},[696],[584,4082,2618],{"className":4083},[763],[584,4085],{"className":4086,"style":759},[696],[584,4088,4090,4093,4096,4125,4128,4131],{"className":4089},[670],[584,4091],{"className":4092,"style":4046},[674],[584,4094,631],{"className":4095},[679],[584,4097,4099,4102],{"className":4098},[679],[584,4100,613],{"className":4101},[679,680],[584,4103,4105],{"className":4104},[724],[584,4106,4108],{"className":4107},[728],[584,4109,4111],{"className":4110},[732],[584,4112,4114],{"className":4113,"style":4065},[736],[584,4115,4116,4119],{"style":4068},[584,4117],{"className":4118,"style":745},[744],[584,4120,4122],{"className":4121},[749,750,751,752],[584,4123,644],{"className":4124},[679,752],[584,4126],{"className":4127,"style":759},[696],[584,4129,634],{"className":4130},[763],[584,4132],{"className":4133,"style":759},[696],[584,4135,4137,4140],{"className":4136},[670],[584,4138],{"className":4139,"style":872},[674],[584,4141,1086],{"className":4142},[679],[565,4144,4145,4146,944,4211,944,4309,944,4411,4481,4482,4613,4614,4674,4675,4613,4845,4895],{},"Probe: ",[584,4147,4149,4172],{"className":4148},[587],[584,4150,4152],{"className":4151},[591],[593,4153,4154],{"xmlns":595},[597,4155,4156,4170],{},[600,4157,4158,4160,4162,4164,4166,4168],{},[603,4159,605],{},[607,4161,610],{"stretchy":609},[629,4163,1202],{},[607,4165,616],{"stretchy":609},[607,4167,619],{},[629,4169,1086],{},[658,4171,3034],{"encoding":660},[584,4173,4175,4202],{"className":4174,"ariaHidden":666},[665],[584,4176,4178,4181,4184,4187,4190,4193,4196,4199],{"className":4177},[670],[584,4179],{"className":4180,"style":675},[674],[584,4182,605],{"className":4183,"style":681},[679,680],[584,4185,610],{"className":4186},[685],[584,4188,1202],{"className":4189},[679],[584,4191,616],{"className":4192},[692],[584,4194],{"className":4195,"style":697},[696],[584,4197,619],{"className":4198},[701],[584,4200],{"className":4201,"style":697},[696],[584,4203,4205,4208],{"className":4204},[670],[584,4206],{"className":4207,"style":872},[674],[584,4209,1086],{"className":4210},[679],[584,4212,4214,4241],{"className":4213},[587],[584,4215,4217],{"className":4216},[591],[593,4218,4219],{"xmlns":595},[597,4220,4221,4239],{},[600,4222,4223,4229,4231,4233,4235,4237],{},[624,4224,4225,4227],{},[603,4226,605],{},[607,4228,897],{"mathvariant":895,"lspace":896,"rspace":896},[607,4230,610],{"stretchy":609},[629,4232,1202],{},[607,4234,616],{"stretchy":609},[607,4236,619],{},[629,4238,1202],{},[658,4240,3157],{"encoding":660},[584,4242,4244,4300],{"className":4243,"ariaHidden":666},[665],[584,4245,4247,4250,4282,4285,4288,4291,4294,4297],{"className":4246},[670],[584,4248],{"className":4249,"style":1612},[674],[584,4251,4253,4256],{"className":4252},[679],[584,4254,605],{"className":4255,"style":681},[679,680],[584,4257,4259],{"className":4258},[724],[584,4260,4262],{"className":4261},[728],[584,4263,4265],{"className":4264},[732],[584,4266,4268],{"className":4267,"style":929},[736],[584,4269,4270,4273],{"style":740},[584,4271],{"className":4272,"style":745},[744],[584,4274,4276],{"className":4275},[749,750,751,752],[584,4277,4279],{"className":4278},[679,752],[584,4280,897],{"className":4281},[679,752],[584,4283,610],{"className":4284},[685],[584,4286,1202],{"className":4287},[679],[584,4289,616],{"className":4290},[692],[584,4292],{"className":4293,"style":697},[696],[584,4295,619],{"className":4296},[701],[584,4298],{"className":4299,"style":697},[696],[584,4301,4303,4306],{"className":4302},[670],[584,4304],{"className":4305,"style":872},[674],[584,4307,1202],{"className":4308},[679],[584,4310,4312,4343],{"className":4311},[587],[584,4313,4315],{"className":4314},[591],[593,4316,4317],{"xmlns":595},[597,4318,4319,4341],{},[600,4320,4321,4331,4333,4335,4337,4339],{},[624,4322,4323,4325],{},[603,4324,605],{},[600,4326,4327,4329],{},[607,4328,897],{"mathvariant":895},[607,4330,897],{"mathvariant":895},[607,4332,610],{"stretchy":609},[629,4334,1086],{},[607,4336,616],{"stretchy":609},[607,4338,619],{},[629,4340,1202],{},[658,4342,3313],{"encoding":660},[584,4344,4346,4402],{"className":4345,"ariaHidden":666},[665],[584,4347,4349,4352,4384,4387,4390,4393,4396,4399],{"className":4348},[670],[584,4350],{"className":4351,"style":1612},[674],[584,4353,4355,4358],{"className":4354},[679],[584,4356,605],{"className":4357,"style":681},[679,680],[584,4359,4361],{"className":4360},[724],[584,4362,4364],{"className":4363},[728],[584,4365,4367],{"className":4366},[732],[584,4368,4370],{"className":4369,"style":929},[736],[584,4371,4372,4375],{"style":740},[584,4373],{"className":4374,"style":745},[744],[584,4376,4378],{"className":4377},[749,750,751,752],[584,4379,4381],{"className":4380},[679,752],[584,4382,1011],{"className":4383},[679,752],[584,4385,610],{"className":4386},[685],[584,4388,1086],{"className":4389},[679],[584,4391,616],{"className":4392},[692],[584,4394],{"className":4395,"style":697},[696],[584,4397,619],{"className":4398},[701],[584,4400],{"className":4401,"style":697},[696],[584,4403,4405,4408],{"className":4404},[670],[584,4406],{"className":4407,"style":872},[674],[584,4409,1202],{"className":4410},[679],[584,4412,4414,4439],{"className":4413},[587],[584,4415,4417],{"className":4416},[591],[593,4418,4419],{"xmlns":595},[597,4420,4421,4437],{},[600,4422,4423,4425,4427,4429,4431,4433,4435],{},[603,4424,605],{},[607,4426,610],{"stretchy":609},[629,4428,644],{},[607,4430,616],{"stretchy":609},[607,4432,619],{},[607,4434,2618],{},[629,4436,631],{},[658,4438,3557],{"encoding":660},[584,4440,4442,4469],{"className":4441,"ariaHidden":666},[665],[584,4443,4445,4448,4451,4454,4457,4460,4463,4466],{"className":4444},[670],[584,4446],{"className":4447,"style":675},[674],[584,4449,605],{"className":4450,"style":681},[679,680],[584,4452,610],{"className":4453},[685],[584,4455,644],{"className":4456},[679],[584,4458,616],{"className":4459},[692],[584,4461],{"className":4462,"style":697},[696],[584,4464,619],{"className":4465},[701],[584,4467],{"className":4468,"style":697},[696],[584,4470,4472,4475,4478],{"className":4471},[670],[584,4473],{"className":4474,"style":2972},[674],[584,4476,2618],{"className":4477},[679],[584,4479,631],{"className":4480},[679],". Wegen ",[584,4483,4485,4524],{"className":4484},[587],[584,4486,4488],{"className":4487},[591],[593,4489,4490],{"xmlns":595},[597,4491,4492,4521],{},[600,4493,4494,4504,4506,4508,4510,4512,4514,4516,4519],{},[624,4495,4496,4498],{},[603,4497,605],{},[600,4499,4500,4502],{},[607,4501,897],{"mathvariant":895},[607,4503,897],{"mathvariant":895},[607,4505,610],{"stretchy":609},[629,4507,1202],{},[607,4509,616],{"stretchy":609},[607,4511,619],{},[607,4513,2618],{},[629,4515,2893],{},[607,4517,4518],{},"\u003C",[629,4520,1202],{},[658,4522,4523],{"encoding":660},"f''(0) = -6 \u003C 0",[584,4525,4527,4583,4604],{"className":4526,"ariaHidden":666},[665],[584,4528,4530,4533,4565,4568,4571,4574,4577,4580],{"className":4529},[670],[584,4531],{"className":4532,"style":1612},[674],[584,4534,4536,4539],{"className":4535},[679],[584,4537,605],{"className":4538,"style":681},[679,680],[584,4540,4542],{"className":4541},[724],[584,4543,4545],{"className":4544},[728],[584,4546,4548],{"className":4547},[732],[584,4549,4551],{"className":4550,"style":929},[736],[584,4552,4553,4556],{"style":740},[584,4554],{"className":4555,"style":745},[744],[584,4557,4559],{"className":4558},[749,750,751,752],[584,4560,4562],{"className":4561},[679,752],[584,4563,1011],{"className":4564},[679,752],[584,4566,610],{"className":4567},[685],[584,4569,1202],{"className":4570},[679],[584,4572,616],{"className":4573},[692],[584,4575],{"className":4576,"style":697},[696],[584,4578,619],{"className":4579},[701],[584,4581],{"className":4582,"style":697},[696],[584,4584,4586,4589,4592,4595,4598,4601],{"className":4585},[670],[584,4587],{"className":4588,"style":2972},[674],[584,4590,2618],{"className":4591},[679],[584,4593,2893],{"className":4594},[679],[584,4596],{"className":4597,"style":697},[696],[584,4599,4518],{"className":4600},[701],[584,4602],{"className":4603,"style":697},[696],[584,4605,4607,4610],{"className":4606},[670],[584,4608],{"className":4609,"style":872},[674],[584,4611,1202],{"className":4612},[679]," ist ",[584,4615,4617,4638],{"className":4616},[587],[584,4618,4620],{"className":4619},[591],[593,4621,4622],{"xmlns":595},[597,4623,4624,4636],{},[600,4625,4626,4628,4630,4632,4634],{},[607,4627,610],{"stretchy":609},[629,4629,1202],{},[607,4631,1205],{},[629,4633,1086],{},[607,4635,616],{"stretchy":609},[658,4637,2508],{"encoding":660},[584,4639,4641,4662],{"className":4640,"ariaHidden":666},[665],[584,4642,4644,4647,4650,4653,4656,4659],{"className":4643},[670],[584,4645],{"className":4646,"style":675},[674],[584,4648,610],{"className":4649},[685],[584,4651,1202],{"className":4652},[679],[584,4654],{"className":4655,"style":697},[696],[584,4657,1205],{"className":4658},[701],[584,4660],{"className":4661,"style":697},[696],[584,4663,4665,4668,4671],{"className":4664},[670],[584,4666],{"className":4667,"style":675},[674],[584,4669,1086],{"className":4670},[679],[584,4672,616],{"className":4673},[692]," tatsächlich ein Hochpunkt, und wegen ",[584,4676,4678,4717],{"className":4677},[587],[584,4679,4681],{"className":4680},[591],[593,4682,4683],{"xmlns":595},[597,4684,4685,4714],{},[600,4686,4687,4699,4701,4703,4705,4707,4709,4712],{},[624,4688,4689,4691],{},[603,4690,605],{},[600,4692,4693,4695,4697],{},[607,4694,897],{"mathvariant":895},[607,4696,897],{"mathvariant":895},[607,4698,897],{"mathvariant":895},[607,4700,610],{"stretchy":609},[629,4702,1086],{},[607,4704,616],{"stretchy":609},[607,4706,619],{},[629,4708,2893],{},[607,4710,4711],{"mathvariant":895},"≠",[629,4713,1202],{},[658,4715,4716],{"encoding":660},"f'''(1) = 6 \\neq 0",[584,4718,4720,4777,4836],{"className":4719,"ariaHidden":666},[665],[584,4721,4723,4726,4759,4762,4765,4768,4771,4774],{"className":4722},[670],[584,4724],{"className":4725,"style":1612},[674],[584,4727,4729,4732],{"className":4728},[679],[584,4730,605],{"className":4731,"style":681},[679,680],[584,4733,4735],{"className":4734},[724],[584,4736,4738],{"className":4737},[728],[584,4739,4741],{"className":4740},[732],[584,4742,4744],{"className":4743,"style":929},[736],[584,4745,4746,4749],{"style":740},[584,4747],{"className":4748,"style":745},[744],[584,4750,4752],{"className":4751},[749,750,751,752],[584,4753,4755],{"className":4754},[679,752],[584,4756,4758],{"className":4757},[679,752],"′′′",[584,4760,610],{"className":4761},[685],[584,4763,1086],{"className":4764},[679],[584,4766,616],{"className":4767},[692],[584,4769],{"className":4770,"style":697},[696],[584,4772,619],{"className":4773},[701],[584,4775],{"className":4776,"style":697},[696],[584,4778,4780,4784,4787,4790,4833],{"className":4779},[670],[584,4781],{"className":4782,"style":4783},[674],"height:0.8889em;vertical-align:-0.1944em;",[584,4785,2893],{"className":4786},[679],[584,4788],{"className":4789,"style":697},[696],[584,4791,4793,4826,4830],{"className":4792},[701],[584,4794,4796],{"className":4795},[701],[584,4797,4800],{"className":4798},[679,4799],"vbox",[584,4801,4804],{"className":4802},[4803],"thinbox",[584,4805,4808,4811,4822],{"className":4806},[4807],"rlap",[584,4809],{"className":4810,"style":4783},[674],[584,4812,4815],{"className":4813},[4814],"inner",[584,4816,4818],{"className":4817},[679],[584,4819,4821],{"className":4820},[701],"",[584,4823],{"className":4824},[4825],"fix",[584,4827],{"className":4828},[696,4829],"nobreak",[584,4831,619],{"className":4832},[701],[584,4834],{"className":4835,"style":697},[696],[584,4837,4839,4842],{"className":4838},[670],[584,4840],{"className":4841,"style":872},[674],[584,4843,1202],{"className":4844},[679],[584,4846,4848,4865],{"className":4847},[587],[584,4849,4851],{"className":4850},[591],[593,4852,4853],{"xmlns":595},[597,4854,4855,4863],{},[600,4856,4857,4859,4861],{},[603,4858,613],{},[607,4860,619],{},[629,4862,1086],{},[658,4864,2566],{"encoding":660},[584,4866,4868,4886],{"className":4867,"ariaHidden":666},[665],[584,4869,4871,4874,4877,4880,4883],{"className":4870},[670],[584,4872],{"className":4873,"style":1063},[674],[584,4875,613],{"className":4876},[679,680],[584,4878],{"className":4879,"style":697},[696],[584,4881,619],{"className":4882},[701],[584,4884],{"className":4885,"style":697},[696],[584,4887,4889,4892],{"className":4888},[670],[584,4890],{"className":4891,"style":872},[674],[584,4893,1086],{"className":4894},[679]," tatsächlich eine Wendestelle.",[565,4897,4898,4899,4971,4972,3003],{},"Gesucht ist eine zum Ursprung punktsymmetrische Funktion 3. Grades mit Tiefpunkt ",[584,4900,4902,4929],{"className":4901},[587],[584,4903,4905],{"className":4904},[591],[593,4906,4907],{"xmlns":595},[597,4908,4909,4926],{},[600,4910,4911,4914,4916,4918,4920,4922,4924],{},[603,4912,4913],{},"T",[607,4915,610],{"stretchy":609},[629,4917,1086],{},[607,4919,1205],{},[607,4921,2618],{},[629,4923,644],{},[607,4925,616],{"stretchy":609},[658,4927,4928],{"encoding":660},"T(1 \\mid -2)",[584,4930,4932,4956],{"className":4931,"ariaHidden":666},[665],[584,4933,4935,4938,4941,4944,4947,4950,4953],{"className":4934},[670],[584,4936],{"className":4937,"style":675},[674],[584,4939,4913],{"className":4940,"style":1230},[679,680],[584,4942,610],{"className":4943},[685],[584,4945,1086],{"className":4946},[679],[584,4948],{"className":4949,"style":697},[696],[584,4951,1205],{"className":4952},[701],[584,4954],{"className":4955,"style":697},[696],[584,4957,4959,4962,4965,4968],{"className":4958},[670],[584,4960],{"className":4961,"style":675},[674],[584,4963,2618],{"className":4964},[679],[584,4966,644],{"className":4967},[679],[584,4969,616],{"className":4970},[692],". Ansatz ",[584,4973,4975,5011],{"className":4974},[587],[584,4976,4978],{"className":4977},[591],[593,4979,4980],{"xmlns":595},[597,4981,4982,5008],{},[600,4983,4984,4986,4988,4990,4992,4994,4996,5002,5004,5006],{},[603,4985,605],{},[607,4987,610],{"stretchy":609},[603,4989,613],{},[607,4991,616],{"stretchy":609},[607,4993,619],{},[603,4995,622],{},[624,4997,4998,5000],{},[603,4999,613],{},[629,5001,631],{},[607,5003,634],{},[603,5005,649],{},[603,5007,613],{},[658,5009,5010],{"encoding":660},"f(x) = ax^3 + cx",[584,5012,5014,5041,5088],{"className":5013,"ariaHidden":666},[665],[584,5015,5017,5020,5023,5026,5029,5032,5035,5038],{"className":5016},[670],[584,5018],{"className":5019,"style":675},[674],[584,5021,605],{"className":5022,"style":681},[679,680],[584,5024,610],{"className":5025},[685],[584,5027,613],{"className":5028},[679,680],[584,5030,616],{"className":5031},[692],[584,5033],{"className":5034,"style":697},[696],[584,5036,619],{"className":5037},[701],[584,5039],{"className":5040,"style":697},[696],[584,5042,5044,5047,5050,5079,5082,5085],{"className":5043},[670],[584,5045],{"className":5046,"style":711},[674],[584,5048,622],{"className":5049},[679,680],[584,5051,5053,5056],{"className":5052},[679],[584,5054,613],{"className":5055},[679,680],[584,5057,5059],{"className":5058},[724],[584,5060,5062],{"className":5061},[728],[584,5063,5065],{"className":5064},[732],[584,5066,5068],{"className":5067,"style":737},[736],[584,5069,5070,5073],{"style":740},[584,5071],{"className":5072,"style":745},[744],[584,5074,5076],{"className":5075},[749,750,751,752],[584,5077,631],{"className":5078},[679,752],[584,5080],{"className":5081,"style":759},[696],[584,5083,634],{"className":5084},[763],[584,5086],{"className":5087,"style":759},[696],[584,5089,5091,5094,5097],{"className":5090},[670],[584,5092],{"className":5093,"style":1063},[674],[584,5095,649],{"className":5096},[679,680],[584,5098,613],{"className":5099},[679,680],[1173,5101,5102,5253],{},[577,5103,5104,1567,5175],{},[584,5105,5107,5133],{"className":5106},[587],[584,5108,5110],{"className":5109},[591],[593,5111,5112],{"xmlns":595},[597,5113,5114,5130],{},[600,5115,5116,5118,5120,5122,5124,5126,5128],{},[603,5117,605],{},[607,5119,610],{"stretchy":609},[629,5121,1086],{},[607,5123,616],{"stretchy":609},[607,5125,619],{},[607,5127,2618],{},[629,5129,644],{},[658,5131,5132],{"encoding":660},"f(1) = -2",[584,5134,5136,5163],{"className":5135,"ariaHidden":666},[665],[584,5137,5139,5142,5145,5148,5151,5154,5157,5160],{"className":5138},[670],[584,5140],{"className":5141,"style":675},[674],[584,5143,605],{"className":5144,"style":681},[679,680],[584,5146,610],{"className":5147},[685],[584,5149,1086],{"className":5150},[679],[584,5152,616],{"className":5153},[692],[584,5155],{"className":5156,"style":697},[696],[584,5158,619],{"className":5159},[701],[584,5161],{"className":5162,"style":697},[696],[584,5164,5166,5169,5172],{"className":5165},[670],[584,5167],{"className":5168,"style":2972},[674],[584,5170,2618],{"className":5171},[679],[584,5173,644],{"className":5174},[679],[584,5176,5178,5202],{"className":5177},[587],[584,5179,5181],{"className":5180},[591],[593,5182,5183],{"xmlns":595},[597,5184,5185,5199],{},[600,5186,5187,5189,5191,5193,5195,5197],{},[603,5188,622],{},[607,5190,634],{},[603,5192,649],{},[607,5194,619],{},[607,5196,2618],{},[629,5198,644],{},[658,5200,5201],{"encoding":660},"a + c = -2",[584,5203,5205,5223,5241],{"className":5204,"ariaHidden":666},[665],[584,5206,5208,5211,5214,5217,5220],{"className":5207},[670],[584,5209],{"className":5210,"style":820},[674],[584,5212,622],{"className":5213},[679,680],[584,5215],{"className":5216,"style":759},[696],[584,5218,634],{"className":5219},[763],[584,5221],{"className":5222,"style":759},[696],[584,5224,5226,5229,5232,5235,5238],{"className":5225},[670],[584,5227],{"className":5228,"style":1063},[674],[584,5230,649],{"className":5231},[679,680],[584,5233],{"className":5234,"style":697},[696],[584,5236,619],{"className":5237},[701],[584,5239],{"className":5240,"style":697},[696],[584,5242,5244,5247,5250],{"className":5243},[670],[584,5245],{"className":5246,"style":2972},[674],[584,5248,2618],{"className":5249},[679],[584,5251,644],{"className":5252},[679],[577,5254,5255,1567,5354],{},[584,5256,5258,5286],{"className":5257},[587],[584,5259,5261],{"className":5260},[591],[593,5262,5263],{"xmlns":595},[597,5264,5265,5283],{},[600,5266,5267,5273,5275,5277,5279,5281],{},[624,5268,5269,5271],{},[603,5270,605],{},[607,5272,897],{"mathvariant":895,"lspace":896,"rspace":896},[607,5274,610],{"stretchy":609},[629,5276,1086],{},[607,5278,616],{"stretchy":609},[607,5280,619],{},[629,5282,1202],{},[658,5284,5285],{"encoding":660},"f'(1) = 0",[584,5287,5289,5345],{"className":5288,"ariaHidden":666},[665],[584,5290,5292,5295,5327,5330,5333,5336,5339,5342],{"className":5291},[670],[584,5293],{"className":5294,"style":1612},[674],[584,5296,5298,5301],{"className":5297},[679],[584,5299,605],{"className":5300,"style":681},[679,680],[584,5302,5304],{"className":5303},[724],[584,5305,5307],{"className":5306},[728],[584,5308,5310],{"className":5309},[732],[584,5311,5313],{"className":5312,"style":929},[736],[584,5314,5315,5318],{"style":740},[584,5316],{"className":5317,"style":745},[744],[584,5319,5321],{"className":5320},[749,750,751,752],[584,5322,5324],{"className":5323},[679,752],[584,5325,897],{"className":5326},[679,752],[584,5328,610],{"className":5329},[685],[584,5331,1086],{"className":5332},[679],[584,5334,616],{"className":5335},[692],[584,5337],{"className":5338,"style":697},[696],[584,5340,619],{"className":5341},[701],[584,5343],{"className":5344,"style":697},[696],[584,5346,5348,5351],{"className":5347},[670],[584,5349],{"className":5350,"style":872},[674],[584,5352,1202],{"className":5353},[679],[584,5355,5357,5381],{"className":5356},[587],[584,5358,5360],{"className":5359},[591],[593,5361,5362],{"xmlns":595},[597,5363,5364,5378],{},[600,5365,5366,5368,5370,5372,5374,5376],{},[629,5367,631],{},[603,5369,622],{},[607,5371,634],{},[603,5373,649],{},[607,5375,619],{},[629,5377,1202],{},[658,5379,5380],{"encoding":660},"3a + c = 0",[584,5382,5384,5405,5423],{"className":5383,"ariaHidden":666},[665],[584,5385,5387,5390,5393,5396,5399,5402],{"className":5386},[670],[584,5388],{"className":5389,"style":2972},[674],[584,5391,631],{"className":5392},[679],[584,5394,622],{"className":5395},[679,680],[584,5397],{"className":5398,"style":759},[696],[584,5400,634],{"className":5401},[763],[584,5403],{"className":5404,"style":759},[696],[584,5406,5408,5411,5414,5417,5420],{"className":5407},[670],[584,5409],{"className":5410,"style":1063},[674],[584,5412,649],{"className":5413},[679,680],[584,5415],{"className":5416,"style":697},[696],[584,5418,619],{"className":5419},[701],[584,5421],{"className":5422,"style":697},[696],[584,5424,5426,5429],{"className":5425},[670],[584,5427],{"className":5428,"style":872},[674],[584,5430,1202],{"className":5431},[679],[565,5433,5434,5435,3465,5491,2860,5541,5597,5598,5721,5722,5849],{},"Subtrahieren ergibt ",[584,5436,5438,5458],{"className":5437},[587],[584,5439,5441],{"className":5440},[591],[593,5442,5443],{"xmlns":595},[597,5444,5445,5455],{},[600,5446,5447,5449,5451,5453],{},[629,5448,644],{},[603,5450,622],{},[607,5452,619],{},[629,5454,644],{},[658,5456,5457],{"encoding":660},"2a = 2",[584,5459,5461,5482],{"className":5460,"ariaHidden":666},[665],[584,5462,5464,5467,5470,5473,5476,5479],{"className":5463},[670],[584,5465],{"className":5466,"style":872},[674],[584,5468,644],{"className":5469},[679],[584,5471,622],{"className":5472},[679,680],[584,5474],{"className":5475,"style":697},[696],[584,5477,619],{"className":5478},[701],[584,5480],{"className":5481,"style":697},[696],[584,5483,5485,5488],{"className":5484},[670],[584,5486],{"className":5487,"style":872},[674],[584,5489,644],{"className":5490},[679],[584,5492,5494,5511],{"className":5493},[587],[584,5495,5497],{"className":5496},[591],[593,5498,5499],{"xmlns":595},[597,5500,5501,5509],{},[600,5502,5503,5505,5507],{},[603,5504,622],{},[607,5506,619],{},[629,5508,1086],{},[658,5510,3873],{"encoding":660},[584,5512,5514,5532],{"className":5513,"ariaHidden":666},[665],[584,5515,5517,5520,5523,5526,5529],{"className":5516},[670],[584,5518],{"className":5519,"style":1063},[674],[584,5521,622],{"className":5522},[679,680],[584,5524],{"className":5525,"style":697},[696],[584,5527,619],{"className":5528},[701],[584,5530],{"className":5531,"style":697},[696],[584,5533,5535,5538],{"className":5534},[670],[584,5536],{"className":5537,"style":872},[674],[584,5539,1086],{"className":5540},[679],[584,5542,5544,5564],{"className":5543},[587],[584,5545,5547],{"className":5546},[591],[593,5548,5549],{"xmlns":595},[597,5550,5551,5561],{},[600,5552,5553,5555,5557,5559],{},[603,5554,649],{},[607,5556,619],{},[607,5558,2618],{},[629,5560,631],{},[658,5562,5563],{"encoding":660},"c = -3",[584,5565,5567,5585],{"className":5566,"ariaHidden":666},[665],[584,5568,5570,5573,5576,5579,5582],{"className":5569},[670],[584,5571],{"className":5572,"style":1063},[674],[584,5574,649],{"className":5575},[679,680],[584,5577],{"className":5578,"style":697},[696],[584,5580,619],{"className":5581},[701],[584,5583],{"className":5584,"style":697},[696],[584,5586,5588,5591,5594],{"className":5587},[670],[584,5589],{"className":5590,"style":2972},[674],[584,5592,2618],{"className":5593},[679],[584,5595,631],{"className":5596},[679],", somit ",[584,5599,5601,5635],{"className":5600},[587],[584,5602,5604],{"className":5603},[591],[593,5605,5606],{"xmlns":595},[597,5607,5608,5632],{},[600,5609,5610,5612,5614,5616,5618,5620,5626,5628,5630],{},[603,5611,605],{},[607,5613,610],{"stretchy":609},[603,5615,613],{},[607,5617,616],{"stretchy":609},[607,5619,619],{},[624,5621,5622,5624],{},[603,5623,613],{},[629,5625,631],{},[607,5627,2618],{},[629,5629,631],{},[603,5631,613],{},[658,5633,5634],{"encoding":660},"f(x) = x^3 - 3x",[584,5636,5638,5665,5709],{"className":5637,"ariaHidden":666},[665],[584,5639,5641,5644,5647,5650,5653,5656,5659,5662],{"className":5640},[670],[584,5642],{"className":5643,"style":675},[674],[584,5645,605],{"className":5646,"style":681},[679,680],[584,5648,610],{"className":5649},[685],[584,5651,613],{"className":5652},[679,680],[584,5654,616],{"className":5655},[692],[584,5657],{"className":5658,"style":697},[696],[584,5660,619],{"className":5661},[701],[584,5663],{"className":5664,"style":697},[696],[584,5666,5668,5671,5700,5703,5706],{"className":5667},[670],[584,5669],{"className":5670,"style":711},[674],[584,5672,5674,5677],{"className":5673},[679],[584,5675,613],{"className":5676},[679,680],[584,5678,5680],{"className":5679},[724],[584,5681,5683],{"className":5682},[728],[584,5684,5686],{"className":5685},[732],[584,5687,5689],{"className":5688,"style":737},[736],[584,5690,5691,5694],{"style":740},[584,5692],{"className":5693,"style":745},[744],[584,5695,5697],{"className":5696},[749,750,751,752],[584,5698,631],{"className":5699},[679,752],[584,5701],{"className":5702,"style":759},[696],[584,5704,2618],{"className":5705},[763],[584,5707],{"className":5708,"style":759},[696],[584,5710,5712,5715,5718],{"className":5711},[670],[584,5713],{"className":5714,"style":872},[674],[584,5716,631],{"className":5717},[679],[584,5719,613],{"className":5720},[679,680],". Probe: ",[584,5723,5725,5762],{"className":5724},[587],[584,5726,5728],{"className":5727},[591],[593,5729,5730],{"xmlns":595},[597,5731,5732,5759],{},[600,5733,5734,5744,5746,5748,5750,5752,5754,5757],{},[624,5735,5736,5738],{},[603,5737,605],{},[600,5739,5740,5742],{},[607,5741,897],{"mathvariant":895},[607,5743,897],{"mathvariant":895},[607,5745,610],{"stretchy":609},[629,5747,1086],{},[607,5749,616],{"stretchy":609},[607,5751,619],{},[629,5753,2893],{},[607,5755,5756],{},">",[629,5758,1202],{},[658,5760,5761],{"encoding":660},"f''(1) = 6 > 0",[584,5763,5765,5821,5840],{"className":5764,"ariaHidden":666},[665],[584,5766,5768,5771,5803,5806,5809,5812,5815,5818],{"className":5767},[670],[584,5769],{"className":5770,"style":1612},[674],[584,5772,5774,5777],{"className":5773},[679],[584,5775,605],{"className":5776,"style":681},[679,680],[584,5778,5780],{"className":5779},[724],[584,5781,5783],{"className":5782},[728],[584,5784,5786],{"className":5785},[732],[584,5787,5789],{"className":5788,"style":929},[736],[584,5790,5791,5794],{"style":740},[584,5792],{"className":5793,"style":745},[744],[584,5795,5797],{"className":5796},[749,750,751,752],[584,5798,5800],{"className":5799},[679,752],[584,5801,1011],{"className":5802},[679,752],[584,5804,610],{"className":5805},[685],[584,5807,1086],{"className":5808},[679],[584,5810,616],{"className":5811},[692],[584,5813],{"className":5814,"style":697},[696],[584,5816,619],{"className":5817},[701],[584,5819],{"className":5820,"style":697},[696],[584,5822,5824,5828,5831,5834,5837],{"className":5823},[670],[584,5825],{"className":5826,"style":5827},[674],"height:0.6835em;vertical-align:-0.0391em;",[584,5829,2893],{"className":5830},[679],[584,5832],{"className":5833,"style":697},[696],[584,5835,5756],{"className":5836},[701],[584,5838],{"className":5839,"style":697},[696],[584,5841,5843,5846],{"className":5842},[670],[584,5844],{"className":5845,"style":872},[674],[584,5847,1202],{"className":5848},[679],", es ist ein Tiefpunkt.",[560,5851,5853],{"id":5852},"typische-fehler","Typische Fehler",[1173,5855,5856,6007,6010,6153],{},[577,5857,5858,5859,6006],{},"Bei einem Extrem- oder Wendepunkt nur eine Gleichung aufstellen. Der Punkt liefert ",[584,5860,5862,5893],{"className":5861},[587],[584,5863,5865],{"className":5864},[591],[593,5866,5867],{"xmlns":595},[597,5868,5869,5891],{},[600,5870,5871,5873,5875,5881,5883,5885],{},[603,5872,605],{},[607,5874,610],{"stretchy":609},[1196,5876,5877,5879],{},[603,5878,613],{},[629,5880,1202],{},[607,5882,616],{"stretchy":609},[607,5884,619],{},[1196,5886,5887,5889],{},[603,5888,1210],{},[629,5890,1202],{},[658,5892,1375],{"encoding":660},[584,5894,5896,5960],{"className":5895,"ariaHidden":666},[665],[584,5897,5899,5902,5905,5908,5948,5951,5954,5957],{"className":5898},[670],[584,5900],{"className":5901,"style":675},[674],[584,5903,605],{"className":5904,"style":681},[679,680],[584,5906,610],{"className":5907},[685],[584,5909,5911,5914],{"className":5910},[679],[584,5912,613],{"className":5913},[679,680],[584,5915,5917],{"className":5916},[724],[584,5918,5920,5940],{"className":5919},[728,1246],[584,5921,5923,5937],{"className":5922},[732],[584,5924,5926],{"className":5925,"style":1253},[736],[584,5927,5928,5931],{"style":1256},[584,5929],{"className":5930,"style":745},[744],[584,5932,5934],{"className":5933},[749,750,751,752],[584,5935,1202],{"className":5936},[679,752],[584,5938,1270],{"className":5939},[1269],[584,5941,5943],{"className":5942},[732],[584,5944,5946],{"className":5945,"style":1277},[736],[584,5947],{},[584,5949,616],{"className":5950},[692],[584,5952],{"className":5953,"style":697},[696],[584,5955,619],{"className":5956},[701],[584,5958],{"className":5959,"style":697},[696],[584,5961,5963,5966],{"className":5962},[670],[584,5964],{"className":5965,"style":1449},[674],[584,5967,5969,5972],{"className":5968},[679],[584,5970,1210],{"className":5971,"style":1301},[679,680],[584,5973,5975],{"className":5974},[724],[584,5976,5978,5998],{"className":5977},[728,1246],[584,5979,5981,5995],{"className":5980},[732],[584,5982,5984],{"className":5983,"style":1253},[736],[584,5985,5986,5989],{"style":1316},[584,5987],{"className":5988,"style":745},[744],[584,5990,5992],{"className":5991},[749,750,751,752],[584,5993,1202],{"className":5994},[679,752],[584,5996,1270],{"className":5997},[1269],[584,5999,6001],{"className":6000},[732],[584,6002,6004],{"className":6003,"style":1277},[736],[584,6005],{},", die Eigenschaft eine zweite Gleichung.",[577,6008,6009],{},"Zu wenige oder abhängige Bedingungen verwenden. Dann ist das Gleichungssystem nicht eindeutig lösbar.",[577,6011,6012,6013,6152],{},"Die Probe weglassen. ",[584,6014,6016,6047],{"className":6015},[587],[584,6017,6019],{"className":6018},[591],[593,6020,6021],{"xmlns":595},[597,6022,6023,6045],{},[600,6024,6025,6031,6033,6039,6041,6043],{},[624,6026,6027,6029],{},[603,6028,605],{},[607,6030,897],{"mathvariant":895,"lspace":896,"rspace":896},[607,6032,610],{"stretchy":609},[1196,6034,6035,6037],{},[603,6036,613],{},[603,6038,1511],{},[607,6040,616],{"stretchy":609},[607,6042,619],{},[629,6044,1202],{},[658,6046,1602],{"encoding":660},[584,6048,6050,6143],{"className":6049,"ariaHidden":666},[665],[584,6051,6053,6056,6088,6091,6131,6134,6137,6140],{"className":6052},[670],[584,6054],{"className":6055,"style":1612},[674],[584,6057,6059,6062],{"className":6058},[679],[584,6060,605],{"className":6061,"style":681},[679,680],[584,6063,6065],{"className":6064},[724],[584,6066,6068],{"className":6067},[728],[584,6069,6071],{"className":6070},[732],[584,6072,6074],{"className":6073,"style":929},[736],[584,6075,6076,6079],{"style":740},[584,6077],{"className":6078,"style":745},[744],[584,6080,6082],{"className":6081},[749,750,751,752],[584,6083,6085],{"className":6084},[679,752],[584,6086,897],{"className":6087},[679,752],[584,6089,610],{"className":6090},[685],[584,6092,6094,6097],{"className":6093},[679],[584,6095,613],{"className":6096},[679,680],[584,6098,6100],{"className":6099},[724],[584,6101,6103,6123],{"className":6102},[728,1246],[584,6104,6106,6120],{"className":6105},[732],[584,6107,6109],{"className":6108,"style":1543},[736],[584,6110,6111,6114],{"style":1256},[584,6112],{"className":6113,"style":745},[744],[584,6115,6117],{"className":6116},[749,750,751,752],[584,6118,1511],{"className":6119,"style":1555},[679,680,752],[584,6121,1270],{"className":6122},[1269],[584,6124,6126],{"className":6125},[732],[584,6127,6129],{"className":6128,"style":1277},[736],[584,6130],{},[584,6132,616],{"className":6133},[692],[584,6135],{"className":6136,"style":697},[696],[584,6138,619],{"className":6139},[701],[584,6141],{"className":6142,"style":697},[696],[584,6144,6146,6149],{"className":6145},[670],[584,6147],{"className":6148,"style":872},[674],[584,6150,1202],{"className":6151},[679]," ist nur notwendig, die gefundene Funktion kann an der Stelle auch einen Sattelpunkt haben.",[577,6154,6155],{},"Symmetrie nicht nutzen und so unnötig viele Unbekannte mitschleppen.",{"title":6157,"searchDepth":6158,"depth":6158,"links":6159},"",2,[6160,6161,6162],{"id":562,"depth":6158,"text":563},{"id":2479,"depth":6158,"text":2480},{"id":5852,"depth":6158,"text":5853},[6164,6166,6169,6173,6176,6180,6182,6185,6187,6190,6192],{"lhs":6165,"rhs":1202},"6*1 + 2*(-3)",{"lhs":6167,"rhs":6168},"8*1 + 4*(-3) + 1","-3",{"lhs":6170,"rhs":1086,"where":6171},"x^3 - 3*x^2 + 1",{"x":6172},0,{"lhs":6174,"rhs":1202,"where":6175},"3*x^2 - 6*x",{"x":6172},{"lhs":6177,"rhs":1202,"where":6178},"6*x - 6",{"x":6179},1,{"lhs":6170,"rhs":6168,"where":6181},{"x":6158},{"lhs":6183,"rhs":6184},"6*0 - 6","-6",{"lhs":6186,"rhs":2893},"6*1",{"lhs":6188,"rhs":6189},"1 + (-3)","-2",{"lhs":6191,"rhs":1202},"3*1 + (-3)",{"lhs":6186,"rhs":2893},"n + 1 \\text{ unabhängige Bedingungen für eine Funktion vom Grad } n","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n + 1\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6667em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">unabhängige Bedingungen für eine Funktion vom Grad\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md",{"caption":6198,"x":6199,"y":6202,"unit":6205,"unitY":6206,"axes":6207,"items":6208},"Graph von f(x) = x³ − 3x² + 1 mit dem Hochpunkt (0 | 1), der Wendestelle x = 1 und dem Punkt (2 | −3)",[6200,6201],-1.3,3.4,[6203,6204],-3.9,2.2,52,40,true,[6209,6211,6218,6225,6232],{"type":6210,"expr":6170},"function",{"type":6212,"at":6213,"label":6214,"offset":6215},"point",[6172,6179],"(0 | 1)",[6216,6217],8,-12,{"type":6212,"at":6219,"label":6221,"offset":6222},[6179,6220],-1,"(1 | −1)",[6223,6224],10,-2,{"type":6212,"at":6226,"label":6228,"offset":6229},[6158,6227],-3,"(2 | −3)",[6230,6231],-30,16,{"type":6233,"at":6234,"text":605},"label",[6235,6236],2.6,1.6,"\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 244.4 244\" width=\"244.4\" height=\"244\" role=\"img\" aria-label=\"Graph von f(x) = x³ − 3x² + 1 mit dem Hochpunkt (0 | 1), der Wendestelle x = 1 und dem Punkt (2 | −3)\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-function-reconstruction-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-function-reconstruction-clip\">\u003Crect x=\"0\" y=\"0\" width=\"244.4\" height=\"244\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cline x1=\"0\" y1=\"88\" x2=\"244.4\" y2=\"88\" class=\"fig-axis\" marker-end=\"url(#fig-function-reconstruction-arrow)\"\u002F>\u003Cline x1=\"67.6\" y1=\"244\" x2=\"67.6\" y2=\"0\" class=\"fig-axis\" marker-end=\"url(#fig-function-reconstruction-arrow)\"\u002F>\u003Cline x1=\"15.6\" y1=\"85\" x2=\"15.6\" y2=\"91\" class=\"fig-axis\"\u002F>\u003Ctext x=\"18.6\" y=\"102\" text-anchor=\"start\" class=\"fig-tick\">−1\u003C\u002Ftext>\u003Cline x1=\"119.6\" y1=\"85\" x2=\"119.6\" y2=\"91\" class=\"fig-axis\"\u002F>\u003Ctext x=\"122.6\" y=\"102\" text-anchor=\"start\" class=\"fig-tick\">1\u003C\u002Ftext>\u003Cline x1=\"171.6\" y1=\"85\" x2=\"171.6\" y2=\"91\" class=\"fig-axis\"\u002F>\u003Ctext x=\"174.6\" y=\"102\" text-anchor=\"start\" class=\"fig-tick\">2\u003C\u002Ftext>\u003Cline x1=\"223.6\" y1=\"85\" x2=\"223.6\" y2=\"91\" class=\"fig-axis\"\u002F>\u003Ctext x=\"226.6\" y=\"102\" text-anchor=\"start\" class=\"fig-tick\">3\u003C\u002Ftext>\u003Cline x1=\"64.6\" y1=\"208\" x2=\"70.6\" y2=\"208\" class=\"fig-axis\"\u002F>\u003Ctext x=\"61.599999999999994\" y=\"201\" text-anchor=\"end\" dominant-baseline=\"middle\" class=\"fig-tick\">−3\u003C\u002Ftext>\u003Cline x1=\"64.6\" y1=\"168\" x2=\"70.6\" y2=\"168\" class=\"fig-axis\"\u002F>\u003Ctext x=\"61.599999999999994\" y=\"161\" text-anchor=\"end\" dominant-baseline=\"middle\" class=\"fig-tick\">−2\u003C\u002Ftext>\u003Cline x1=\"64.6\" y1=\"128\" x2=\"70.6\" y2=\"128\" class=\"fig-axis\"\u002F>\u003Ctext x=\"61.599999999999994\" y=\"121\" text-anchor=\"end\" dominant-baseline=\"middle\" class=\"fig-tick\">−1\u003C\u002Ftext>\u003Cline x1=\"64.6\" y1=\"48\" x2=\"70.6\" y2=\"48\" class=\"fig-axis\"\u002F>\u003Ctext x=\"61.599999999999994\" y=\"41\" text-anchor=\"end\" dominant-baseline=\"middle\" class=\"fig-tick\">1\u003C\u002Ftext>\u003Ctext x=\"238.4\" y=\"76\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">x\u003C\u002Ftext>\u003Ctext x=\"79.6\" y=\"8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">y\u003C\u002Ftext>\u003Cpath d=\"M 0 338.68 L 1.02 328.7 L 2.04 318.94 L 3.06 309.38 L 4.07 300.03 L 5.09 290.88 L 6.11 281.94 L 7.13 273.19 L 8.15 264.65 L 9.17 256.3 L 10.18 248.15 L 11.2 240.19 L 12.22 232.42 L 13.24 224.85 L 14.26 217.46 L 15.27 210.26 L 16.29 203.24 L 17.31 196.41 L 18.33 189.76 L 19.35 183.28 L 20.37 176.99 L 21.39 170.87 L 22.4 164.92 L 23.42 159.14 L 24.44 153.54 L 25.46 148.1 L 26.48 142.83 L 27.5 137.73 L 28.51 132.79 L 29.53 128.01 L 30.55 123.39 L 31.57 118.92 L 32.59 114.62 L 33.6 110.46 L 34.62 106.46 L 35.64 102.61 L 36.66 98.91 L 37.68 95.35 L 38.7 91.94 L 39.72 88.68 L 40.73 85.55 L 41.75 82.56 L 42.77 79.72 L 43.79 77 L 44.81 74.43 L 45.83 71.98 L 46.84 69.66 L 47.86 67.48 L 48.88 65.42 L 49.9 63.48 L 50.92 61.67 L 51.94 59.98 L 52.95 58.41 L 53.97 56.96 L 54.99 55.63 L 56.01 54.41 L 57.03 53.3 L 58.05 52.3 L 59.06 51.41 L 60.08 50.63 L 61.1 49.95 L 62.12 49.38 L 63.14 48.91 L 64.16 48.54 L 65.17 48.27 L 66.19 48.09 L 67.21 48.01 L 68.23 48.02 L 69.25 48.12 L 70.27 48.31 L 71.28 48.59 L 72.3 48.95 L 73.32 49.4 L 74.34 49.93 L 75.36 50.54 L 76.38 51.22 L 77.39 51.99 L 78.41 52.83 L 79.43 53.74 L 80.45 54.72 L 81.47 55.77 L 82.49 56.89 L 83.5 58.08 L 84.52 59.33 L 85.54 60.64 L 86.56 62.01 L 87.58 63.44 L 88.6 64.93 L 89.61 66.47 L 90.63 68.07 L 91.65 69.71 L 92.67 71.41 L 93.69 73.15 L 94.71 74.94 L 95.72 76.77 L 96.74 78.65 L 97.76 80.56 L 98.78 82.52 L 99.8 84.51 L 100.82 86.54 L 101.83 88.6 L 102.85 90.69 L 103.87 92.81 L 104.89 94.96 L 105.91 97.13 L 106.93 99.33 L 107.94 101.55 L 108.96 103.79 L 109.98 106.05 L 111 108.33 L 112.02 110.62 L 113.04 112.93 L 114.05 115.25 L 115.07 117.58 L 116.09 119.91 L 117.11 122.25 L 118.13 124.6 L 119.14 126.95 L 120.16 129.3 L 121.18 131.65 L 122.2 134 L 123.22 136.34 L 124.24 138.67 L 125.26 141 L 126.27 143.32 L 127.29 145.62 L 128.31 147.91 L 129.33 150.19 L 130.35 152.45 L 131.37 154.69 L 132.38 156.91 L 133.4 159.1 L 134.42 161.27 L 135.44 163.42 L 136.46 165.54 L 137.48 167.63 L 138.49 169.68 L 139.51 171.7 L 140.53 173.69 L 141.55 175.64 L 142.57 177.55 L 143.59 179.42 L 144.6 181.25 L 145.62 183.04 L 146.64 184.78 L 147.66 186.47 L 148.68 188.11 L 149.7 189.7 L 150.71 191.23 L 151.73 192.71 L 152.75 194.14 L 153.77 195.5 L 154.79 196.81 L 155.81 198.05 L 156.82 199.23 L 157.84 200.34 L 158.86 201.39 L 159.88 202.36 L 160.9 203.26 L 161.92 204.1 L 162.93 204.85 L 163.95 205.53 L 164.97 206.13 L 165.99 206.65 L 167.01 207.09 L 168.03 207.45 L 169.04 207.71 L 170.06 207.9 L 171.08 207.99 L 172.1 207.99 L 173.12 207.9 L 174.14 207.71 L 175.15 207.43 L 176.17 207.05 L 177.19 206.56 L 178.21 205.98 L 179.23 205.29 L 180.24 204.5 L 181.26 203.6 L 182.28 202.59 L 183.3 201.47 L 184.32 200.24 L 185.34 198.89 L 186.36 197.42 L 187.37 195.84 L 188.39 194.14 L 189.41 192.32 L 190.43 190.37 L 191.45 188.3 L 192.47 186.1 L 193.48 183.77 L 194.5 181.31 L 195.52 178.71 L 196.54 175.99 L 197.56 173.12 L 198.58 170.12 L 199.59 166.98 L 200.61 163.7 L 201.63 160.28 L 202.65 156.7 L 203.67 152.99 L 204.69 149.12 L 205.7 145.1 L 206.72 140.93 L 207.74 136.61 L 208.76 132.13 L 209.78 127.49 L 210.8 122.69 L 211.81 117.74 L 212.83 112.61 L 213.85 107.33 L 214.87 101.87 L 215.89 96.25 L 216.9 90.46 L 217.92 84.49 L 218.94 78.35 L 219.96 72.04 L 220.98 65.55 L 222 58.87 L 223.01 52.02 L 224.03 44.98 L 225.05 37.76 L 226.07 30.35 L 227.09 22.76 L 228.11 14.97 L 229.13 6.99 L 230.14 -1.18 L 231.16 -9.55 L 232.18 -18.11 L 233.2 -26.88 L 234.22 -35.84 L 235.24 -45.01 L 236.25 -54.39 L 237.27 -63.97 L 238.29 -73.76 L 239.31 -83.75 L 240.33 -93.96 L 241.35 -104.39 L 242.36 -115.03 L 243.38 -125.88 L 244.4 -136.96\" class=\"fig-main fig-graph\" clip-path=\"url(#fig-function-reconstruction-clip)\"\u002F>\u003Ccircle cx=\"67.6\" cy=\"48\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"75.6\" y=\"36\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">(0 | 1)\u003C\u002Ftext>\u003Ccircle cx=\"119.6\" cy=\"128\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"129.6\" y=\"126\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">(1 | −1)\u003C\u002Ftext>\u003Ccircle cx=\"171.6\" cy=\"208\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"141.6\" y=\"224\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">(2 | −3)\u003C\u002Ftext>\u003Ctext x=\"202.8\" y=\"24\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">f\u003C\u002Ftext>\u003C\u002Fsvg>","function-reconstruction","\\begin{gathered} f(x) = ax^3 + bx^2 + cx + d \\\\ \\text{mit}\\ f(x_0) = y_0, \\\\ f'(x_E) = 0,\\ f''(x_W) = 0 \\end{gathered}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmtable rowspacing=\"0.25em\" columnalign=\"center\" columnspacing=\"0em\">\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"true\">\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>d\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"true\">\u003Cmrow>\u003Cmtext>mit \u003C\u002Fmtext>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>y\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"true\">\u003Cmrow>\u003Cmsup>\u003Cmi>f\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">′\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>E\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmsup>\u003Cmi>f\u003C\u002Fmi>\u003Cmrow>\u003Cmo mathvariant=\"normal\">′\u003C\u002Fmo>\u003Cmo mathvariant=\"normal\">′\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>W\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003C\u002Fmtable>\u003Cannotation encoding=\"application\u002Fx-tex\">\\begin{gathered} f(x) = ax^3 + bx^2 + cx + d \\\\ \\text{mit}\\ f(x_0) = y_0, \\\\ f'(x_E) = 0,\\ f''(x_W) = 0 \\end{gathered}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:4.2241em;vertical-align:-1.8621em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:2.3621em;\">\u003Cspan style=\"top:-4.4979em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">3\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-2.9979em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord text\">\u003Cspan class=\"mord\">mit\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\"> \u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-1.4979em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8019em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">′\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3283em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0576em;\">E\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\"> \u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8019em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">′′\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3283em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.1389em;\">W\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.8621em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},"\u002Fde\u002Fformulas\u002Fmath\u002Fcalculus\u002Fsteckbriefaufgaben",[],[6246,6247,6248,6249],"polynomial-function","extremum-condition","inflection-condition","gaussian-elimination",{"title":548,"description":6157},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fsteckbriefaufgaben","Aus Eigenschaften wie Punkten, Extrem- und Wendestellen stellt man ein Gleichungssystem für die Koeffizienten auf.",[6254,6255,6256,6257],"steckbriefaufgabe","rekonstruktion","ganzrationale funktion","gleichungssystem",[6259,6263,6266,6269,6272],{"symbol":6260,"meaning":6261,"symbolHtml":6262},"a, b, c, d","gesuchte Koeffizienten der ganzrationalen Funktion","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>d\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a, b, c, d\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1375,"meaning":6264,"symbolHtml":6265},"Bedingung aus einem Punkt P(x₀ | y₀) auf dem Graphen","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>y\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f(x_0) = y_0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1514,"meaning":6267,"symbolHtml":6268},"Extremstelle, an der die Ableitung null ist","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>E\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x_E\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3283em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0576em;\">E\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":2035,"meaning":6270,"symbolHtml":6271},"Wendestelle, an der die zweite Ableitung null ist","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>W\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x_W\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3283em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.1389em;\">W\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1051,"meaning":6273,"symbolHtml":6274},"Grad der gesuchten Funktion, Anzahl der Unbekannten ist n + 1","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","-NDBt0IDMRuZt1d1vzzUAii9fu34mzCNjnxAa0rnjwM",[6277,6280,6283,6286],{"stem":6278,"title":6279,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fbedingungen-extremstellen","Bedingungen für Extremstellen",{"stem":6281,"title":6282,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fbedingungen-wendestellen","Bedingungen für Wendestellen",{"stem":6284,"title":6285,"category":208},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fganzrationale-funktion","Ganzrationale Funktion",{"stem":6287,"title":6288,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fgauss-algorithmus","Gauß-Algorithmus",1793824283791]