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0",[572,1060,1062,1197],{"className":1061,"ariaHidden":635},[634],[572,1063,1065,1068,1101,1104,1144,1147,1150,1194],{"className":1064},[639],[572,1066],{"className":1067,"style":915},[643],[572,1069,1071,1074],{"className":1070},[648],[572,1072,612],{"className":1073,"style":732},[648,649],[572,1075,1077],{"className":1076},[664],[572,1078,1080],{"className":1079},[668],[572,1081,1083],{"className":1082},[673],[572,1084,1086],{"className":1085,"style":934},[677],[572,1087,1088,1091],{"style":937},[572,1089],{"className":1090,"style":686},[685],[572,1092,1094],{"className":1093},[690,691,692,693],[572,1095,1097],{"className":1096},[648,693],[572,1098,1100],{"className":1099},[648,693],"′′′",[572,1102,598],{"className":1103},[654],[572,1105,1107,1110],{"className":1106},[648],[572,1108,604],{"className":1109},[648,649],[572,1111,1113],{"className":1112},[664],[572,1114,1116,1136],{"className":1115},[668,669],[572,1117,1119,1133],{"className":1118},[673],[572,1120,1122],{"className":1121,"style":678},[677],[572,1123,1124,1127],{"style":681},[572,1125],{"className":1126,"style":686},[685],[572,1128,1130],{"className":1129},[690,691,692,693],[572,1131,593],{"className":1132,"style":650},[648,649,693],[572,1134,701],{"className":1135},[700],[572,1137,1139],{"className":1138},[673],[572,1140,1142],{"className":1141,"style":708},[677],[572,1143],{},[572,1145,623],{"className":1146},[779],[572,1148],{"className":1149,"style":715},[714],[572,1151,1153,1187,1191],{"className":1152},[719],[572,1154,1156],{"className":1155},[719],[572,1157,1160],{"className":1158},[648,1159],"vbox",[572,1161,1164],{"className":1162},[1163],"thinbox",[572,1165,1168,1172,1183],{"className":1166},[1167],"rlap",[572,1169],{"className":1170,"style":1171},[643],"height:0.8889em;vertical-align:-0.1944em;",[572,1173,1176],{"className":1174},[1175],"inner",[572,1177,1179],{"className":1178},[648],[572,1180,1182],{"className":1181},[719],"",[572,1184],{"className":1185},[1186],"fix",[572,1188],{"className":1189},[714,1190],"nobreak",[572,1192,898],{"className":1193},[719],[572,1195],{"className":1196,"style":715},[714],[572,1198,1200,1203],{"className":1199},[639],[572,1201],{"className":1202,"style":1012},[643],[572,1204,902],{"className":1205},[648]," (oder Vorzeichenwechsel von ",[572,1208,1210,1232],{"className":1209},[575],[572,1211,1213],{"className":1212},[579],[581,1214,1215],{"xmlns":583},[585,1216,1217,1229],{},[588,1218,1219],{},[874,1220,1221,1223],{},[591,1222,612],{},[588,1224,1225,1227],{},[595,1226,883],{"mathvariant":882},[595,1228,883],{"mathvariant":882},[627,1230,1231],{"encoding":629},"f''",[572,1233,1235],{"className":1234,"ariaHidden":635},[634],[572,1236,1238,1242],{"className":1237},[639],[572,1239],{"className":1240,"style":1241},[643],"height:0.9463em;vertical-align:-0.1944em;",[572,1243,1245,1248],{"className":1244},[648],[572,1246,612],{"className":1247,"style":732},[648,649],[572,1249,1251],{"className":1250},[664],[572,1252,1254],{"className":1253},[668],[572,1255,1257],{"className":1256},[673],[572,1258,1260],{"className":1259,"style":934},[677],[572,1261,1262,1265],{"style":937},[572,1263],{"className":1264,"style":686},[685],[572,1266,1268],{"className":1267},[690,691,692,693],[572,1269,1271],{"className":1270},[648,693],[572,1272,950],{"className":1273},[648,693],").",[786,1276,1277,1362,1363,1482],{},[572,1278,1280,1304],{"className":1279},[575],[572,1281,1283],{"className":1282},[579],[581,1284,1285],{"xmlns":583},[585,1286,1287,1301],{},[588,1288,1289,1291,1293,1299],{},[591,1290,612],{},[595,1292,598],{"stretchy":597},[600,1294,1295,1297],{},[591,1296,604],{},[591,1298,593],{},[595,1300,623],{"stretchy":597},[627,1302,1303],{"encoding":629},"f(x_W)",[572,1305,1307],{"className":1306,"ariaHidden":635},[634],[572,1308,1310,1313,1316,1319,1359],{"className":1309},[639],[572,1311],{"className":1312,"style":644},[643],[572,1314,612],{"className":1315,"style":732},[648,649],[572,1317,598],{"className":1318},[654],[572,1320,1322,1325],{"className":1321},[648],[572,1323,604],{"className":1324},[648,649],[572,1326,1328],{"className":1327},[664],[572,1329,1331,1351],{"className":1330},[668,669],[572,1332,1334,1348],{"className":1333},[673],[572,1335,1337],{"className":1336,"style":678},[677],[572,1338,1339,1342],{"style":681},[572,1340],{"className":1341,"style":686},[685],[572,1343,1345],{"className":1344},[690,691,692,693],[572,1346,593],{"className":1347,"style":650},[648,649,693],[572,1349,701],{"className":1350},[700],[572,1352,1354],{"className":1353},[673],[572,1355,1357],{"className":1356,"style":708},[677],[572,1358],{},[572,1360,623],{"className":1361},[779]," und die Steigung ",[572,1364,1366,1395],{"className":1365},[575],[572,1367,1369],{"className":1368},[579],[581,1370,1371],{"xmlns":583},[585,1372,1373,1392],{},[588,1374,1375,1382,1384,1390],{},[874,1376,1377,1379],{},[591,1378,612],{},[595,1380,883],{"mathvariant":882,"lspace":1381,"rspace":1381},"0em",[595,1383,598],{"stretchy":597},[600,1385,1386,1388],{},[591,1387,604],{},[591,1389,593],{},[595,1391,623],{"stretchy":597},[627,1393,1394],{"encoding":629},"f'(x_W)",[572,1396,1398],{"className":1397,"ariaHidden":635},[634],[572,1399,1401,1404,1436,1439,1479],{"className":1400},[639],[572,1402],{"className":1403,"style":915},[643],[572,1405,1407,1410],{"className":1406},[648],[572,1408,612],{"className":1409,"style":732},[648,649],[572,1411,1413],{"className":1412},[664],[572,1414,1416],{"className":1415},[668],[572,1417,1419],{"className":1418},[673],[572,1420,1422],{"className":1421,"style":934},[677],[572,1423,1424,1427],{"style":937},[572,1425],{"className":1426,"style":686},[685],[572,1428,1430],{"className":1429},[690,691,692,693],[572,1431,1433],{"className":1432},[648,693],[572,1434,883],{"className":1435},[648,693],[572,1437,598],{"className":1438},[654],[572,1440,1442,1445],{"className":1441},[648],[572,1443,604],{"className":1444},[648,649],[572,1446,1448],{"className":1447},[664],[572,1449,1451,1471],{"className":1450},[668,669],[572,1452,1454,1468],{"className":1453},[673],[572,1455,1457],{"className":1456,"style":678},[677],[572,1458,1459,1462],{"style":681},[572,1460],{"className":1461,"style":686},[685],[572,1463,1465],{"className":1464},[690,691,692,693],[572,1466,593],{"className":1467,"style":650},[648,649,693],[572,1469,701],{"className":1470},[700],[572,1472,1474],{"className":1473},[673],[572,1475,1477],{"className":1476,"style":708},[677],[572,1478],{},[572,1480,623],{"className":1481},[779]," berechnen.",[786,1484,1485],{},"Beides in die Tangentengleichung einsetzen.",[564,1487,1488,1489,1492],{},"Im Unterschied zu anderen Tangenten ",[568,1490,1491],{},"durchsetzt"," die Wendetangente den Graphen: Auf der einen Seite liegt der Graph oberhalb, auf der anderen unterhalb. Im Wendepunkt ist die Steigung lokal am größten oder am kleinsten, die Wendetangente ist also die steilste oder flachste Tangente in der Umgebung.",[564,1494,1495,1496,1636,1637,1640],{},"Ist ",[572,1497,1499,1531],{"className":1498},[575],[572,1500,1502],{"className":1501},[579],[581,1503,1504],{"xmlns":583},[585,1505,1506,1528],{},[588,1507,1508,1514,1516,1522,1524,1526],{},[874,1509,1510,1512],{},[591,1511,612],{},[595,1513,883],{"mathvariant":882,"lspace":1381,"rspace":1381},[595,1515,598],{"stretchy":597},[600,1517,1518,1520],{},[591,1519,604],{},[591,1521,593],{},[595,1523,623],{"stretchy":597},[595,1525,898],{},[900,1527,902],{},[627,1529,1530],{"encoding":629},"f'(x_W) = 0",[572,1532,1534,1627],{"className":1533,"ariaHidden":635},[634],[572,1535,1537,1540,1572,1575,1615,1618,1621,1624],{"className":1536},[639],[572,1538],{"className":1539,"style":915},[643],[572,1541,1543,1546],{"className":1542},[648],[572,1544,612],{"className":1545,"style":732},[648,649],[572,1547,1549],{"className":1548},[664],[572,1550,1552],{"className":1551},[668],[572,1553,1555],{"className":1554},[673],[572,1556,1558],{"className":1557,"style":934},[677],[572,1559,1560,1563],{"style":937},[572,1561],{"className":1562,"style":686},[685],[572,1564,1566],{"className":1565},[690,691,692,693],[572,1567,1569],{"className":1568},[648,693],[572,1570,883],{"className":1571},[648,693],[572,1573,598],{"className":1574},[654],[572,1576,1578,1581],{"className":1577},[648],[572,1579,604],{"className":1580},[648,649],[572,1582,1584],{"className":1583},[664],[572,1585,1587,1607],{"className":1586},[668,669],[572,1588,1590,1604],{"className":1589},[673],[572,1591,1593],{"className":1592,"style":678},[677],[572,1594,1595,1598],{"style":681},[572,1596],{"className":1597,"style":686},[685],[572,1599,1601],{"className":1600},[690,691,692,693],[572,1602,593],{"className":1603,"style":650},[648,649,693],[572,1605,701],{"className":1606},[700],[572,1608,1610],{"className":1609},[673],[572,1611,1613],{"className":1612,"style":708},[677],[572,1614],{},[572,1616,623],{"className":1617},[779],[572,1619],{"className":1620,"style":715},[714],[572,1622,898],{"className":1623},[719],[572,1625],{"className":1626,"style":715},[714],[572,1628,1630,1633],{"className":1629},[639],[572,1631],{"className":1632,"style":1012},[643],[572,1634,902],{"className":1635},[648],", ist die Wendetangente waagerecht, und der Wendepunkt ist ein ",[568,1638,1639],{},"Sattelpunkt",".",[564,1642,566,1643,1645,1646,1819,1820,1640],{},[568,1644,553],{}," steht im Wendepunkt senkrecht auf der Wendetangente. Für ",[572,1647,1649,1681],{"className":1648},[575],[572,1650,1652],{"className":1651},[579],[581,1653,1654],{"xmlns":583},[585,1655,1656,1678],{},[588,1657,1658,1664,1666,1672,1674,1676],{},[874,1659,1660,1662],{},[591,1661,612],{},[595,1663,883],{"mathvariant":882,"lspace":1381,"rspace":1381},[595,1665,598],{"stretchy":597},[600,1667,1668,1670],{},[591,1669,604],{},[591,1671,593],{},[595,1673,623],{"stretchy":597},[595,1675,1053],{"mathvariant":882},[900,1677,902],{},[627,1679,1680],{"encoding":629},"f'(x_W) \\neq 0",[572,1682,1684,1810],{"className":1683,"ariaHidden":635},[634],[572,1685,1687,1690,1722,1725,1765,1768,1771,1807],{"className":1686},[639],[572,1688],{"className":1689,"style":915},[643],[572,1691,1693,1696],{"className":1692},[648],[572,1694,612],{"className":1695,"style":732},[648,649],[572,1697,1699],{"className":1698},[664],[572,1700,1702],{"className":1701},[668],[572,1703,1705],{"className":1704},[673],[572,1706,1708],{"className":1707,"style":934},[677],[572,1709,1710,1713],{"style":937},[572,1711],{"className":1712,"style":686},[685],[572,1714,1716],{"className":1715},[690,691,692,693],[572,1717,1719],{"className":1718},[648,693],[572,1720,883],{"className":1721},[648,693],[572,1723,598],{"className":1724},[654],[572,1726,1728,1731],{"className":1727},[648],[572,1729,604],{"className":1730},[648,649],[572,1732,1734],{"className":1733},[664],[572,1735,1737,1757],{"className":1736},[668,669],[572,1738,1740,1754],{"className":1739},[673],[572,1741,1743],{"className":1742,"style":678},[677],[572,1744,1745,1748],{"style":681},[572,1746],{"className":1747,"style":686},[685],[572,1749,1751],{"className":1750},[690,691,692,693],[572,1752,593],{"className":1753,"style":650},[648,649,693],[572,1755,701],{"className":1756},[700],[572,1758,1760],{"className":1759},[673],[572,1761,1763],{"className":1762,"style":708},[677],[572,1764],{},[572,1766,623],{"className":1767},[779],[572,1769],{"className":1770,"style":715},[714],[572,1772,1774,1801,1804],{"className":1773},[719],[572,1775,1777],{"className":1776},[719],[572,1778,1780],{"className":1779},[648,1159],[572,1781,1783],{"className":1782},[1163],[572,1784,1786,1789,1798],{"className":1785},[1167],[572,1787],{"className":1788,"style":1171},[643],[572,1790,1792],{"className":1791},[1175],[572,1793,1795],{"className":1794},[648],[572,1796,1182],{"className":1797},[719],[572,1799],{"className":1800},[1186],[572,1802],{"className":1803},[714,1190],[572,1805,898],{"className":1806},[719],[572,1808],{"className":1809,"style":715},[714],[572,1811,1813,1816],{"className":1812},[639],[572,1814],{"className":1815,"style":1012},[643],[572,1817,902],{"className":1818},[648]," hat sie die Steigung 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= -x^3 + 3x^2 + 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und ",[572,2844,2846,2886],{"className":2845},[575],[572,2847,2849],{"className":2848},[579],[581,2850,2851],{"xmlns":583},[585,2852,2853,2883],{},[588,2854,2855,2867,2869,2871,2873,2875,2877,2879,2881],{},[874,2856,2857,2859],{},[591,2858,612],{},[588,2860,2861,2863,2865],{},[595,2862,883],{"mathvariant":882},[595,2864,883],{"mathvariant":882},[595,2866,883],{"mathvariant":882},[595,2868,598],{"stretchy":597},[900,2870,1840],{},[595,2872,623],{"stretchy":597},[595,2874,898],{},[595,2876,1834],{},[900,2878,2269],{},[595,2880,1053],{"mathvariant":882},[900,2882,902],{},[627,2884,2885],{"encoding":629},"f'''(1) = -6 \\neq 0",[572,2887,2889,2945,2999],{"className":2888,"ariaHidden":635},[634],[572,2890,2892,2895,2927,2930,2933,2936,2939,2942],{"className":2891},[639],[572,2893],{"className":2894,"style":915},[643],[572,2896,2898,2901],{"className":2897},[648],[572,2899,612],{"className":2900,"style":732},[648,649],[572,2902,2904],{"className":2903},[664],[572,2905,2907],{"className":2906},[668],[572,2908,2910],{"className":2909},[673],[572,2911,2913],{"className":2912,"style":934},[677],[572,2914,2915,2918],{"style":937},[572,2916],{"className":2917,"style":686},[685],[572,2919,2921],{"className":2920},[690,691,692,693],[572,2922,2924],{"className":2923},[648,693],[572,2925,1100],{"className":2926},[648,693],[572,2928,598],{"className":2929},[654],[572,2931,1840],{"className":2932},[648],[572,2934,623],{"className":2935},[779],[572,2937],{"className":2938,"style":715},[714],[572,2940,898],{"className":2941},[719],[572,2943],{"className":2944,"style":715},[714],[572,2946,2948,2951,2954,2957,2960,2996],{"className":2947},[639],[572,2949],{"className":2950,"style":1171},[643],[572,2952,1834],{"className":2953},[648],[572,2955,2269],{"className":2956},[648],[572,2958],{"className":2959,"style":715},[714],[572,2961,2963,2990,2993],{"className":2962},[719],[572,2964,2966],{"className":2965},[719],[572,2967,2969],{"className":2968},[648,1159],[572,2970,2972],{"className":2971},[1163],[572,2973,2975,2978,2987],{"className":2974},[1167],[572,2976],{"className":2977,"style":1171},[643],[572,2979,2981],{"className":2980},[1175],[572,2982,2984],{"className":2983},[648],[572,2985,1182],{"className":2986},[719],[572,2988],{"className":2989},[1186],[572,2991],{"className":2992},[714,1190],[572,2994,898],{"className":2995},[719],[572,2997],{"className":2998,"style":715},[714],[572,3000,3002,3005],{"className":3001},[639],[572,3003],{"className":3004,"style":1012},[643],[572,3006,902],{"className":3007},[648],". Mit ",[572,3010,3012,3036],{"className":3011},[575],[572,3013,3015],{"className":3014},[579],[581,3016,3017],{"xmlns":583},[585,3018,3019,3033],{},[588,3020,3021,3023,3025,3027,3029,3031],{},[591,3022,612],{},[595,3024,598],{"stretchy":597},[900,3026,1840],{},[595,3028,623],{"stretchy":597},[595,3030,898],{},[900,3032,2071],{},[627,3034,3035],{"encoding":629},"f(1) = 3",[572,3037,3039,3066],{"className":3038,"ariaHidden":635},[634],[572,3040,3042,3045,3048,3051,3054,3057,3060,3063],{"className":3041},[639],[572,3043],{"className":3044,"style":644},[643],[572,3046,612],{"className":3047,"style":732},[648,649],[572,3049,598],{"className":3050},[654],[572,3052,1840],{"className":3053},[648],[572,3055,623],{"className":3056},[779],[572,3058],{"className":3059,"style":715},[714],[572,3061,898],{"className":3062},[719],[572,3064],{"className":3065,"style":715},[714],[572,3067,3069,3072],{"className":3068},[639],[572,3070],{"className":3071,"style":1012},[643],[572,3073,2071],{"className":3074},[648],[572,3076,3078,3106],{"className":3077},[575],[572,3079,3081],{"className":3080},[579],[581,3082,3083],{"xmlns":583},[585,3084,3085,3103],{},[588,3086,3087,3093,3095,3097,3099,3101],{},[874,3088,3089,3091],{},[591,3090,612],{},[595,3092,883],{"mathvariant":882,"lspace":1381,"rspace":1381},[595,3094,598],{"stretchy":597},[900,3096,1840],{},[595,3098,623],{"stretchy":597},[595,3100,898],{},[900,3102,2071],{},[627,3104,3105],{"encoding":629},"f'(1) = 3",[572,3107,3109,3165],{"className":3108,"ariaHidden":635},[634],[572,3110,3112,3115,3147,3150,3153,3156,3159,3162],{"className":3111},[639],[572,3113],{"className":3114,"style":915},[643],[572,3116,3118,3121],{"className":3117},[648],[572,3119,612],{"className":3120,"style":732},[648,649],[572,3122,3124],{"className":3123},[664],[572,3125,3127],{"className":3126},[668],[572,3128,3130],{"className":3129},[673],[572,3131,3133],{"className":3132,"style":934},[677],[572,3134,3135,3138],{"style":937},[572,3136],{"className":3137,"style":686},[685],[572,3139,3141],{"className":3140},[690,691,692,693],[572,3142,3144],{"className":3143},[648,693],[572,3145,883],{"className":3146},[648,693],[572,3148,598],{"className":3149},[654],[572,3151,1840],{"className":3152},[648],[572,3154,623],{"className":3155},[779],[572,3157],{"className":3158,"style":715},[714],[572,3160,898],{"className":3161},[719],[572,3163],{"className":3164,"style":715},[714],[572,3166,3168,3171],{"className":3167},[639],[572,3169],{"className":3170,"style":1012},[643],[572,3172,2071],{"className":3173},[648],":",[572,3176,3179],{"className":3177},[3178],"katex-display",[572,3180,3182,3235],{"className":3181},[575],[572,3183,3185],{"className":3184},[579],[581,3186,3188],{"xmlns":583,"display":3187},"block",[585,3189,3190,3232],{},[588,3191,3192,3199,3201,3203,3205,3207,3209,3212,3214,3216,3218,3220,3222,3224,3226,3228,3230],{},[600,3193,3194,3197],{},[591,3195,3196],{},"t",[591,3198,593],{},[595,3200,598],{"stretchy":597},[591,3202,604],{},[595,3204,623],{"stretchy":597},[595,3206,898],{},[900,3208,2071],{},[595,3210,3211],{},"⋅",[595,3213,598],{"stretchy":597},[591,3215,604],{},[595,3217,1834],{},[900,3219,1840],{},[595,3221,623],{"stretchy":597},[595,3223,2074],{},[900,3225,2071],{},[595,3227,898],{},[900,3229,2071],{},[591,3231,604],{},[627,3233,3234],{"encoding":629},"t_W(x) = 3 \\cdot (x - 1) + 3 = 3x",[572,3236,3238,3302,3320,3341,3362,3380],{"className":3237,"ariaHidden":635},[634],[572,3239,3241,3244,3284,3287,3290,3293,3296,3299],{"className":3240},[639],[572,3242],{"className":3243,"style":644},[643],[572,3245,3247,3250],{"className":3246},[648],[572,3248,3196],{"className":3249},[648,649],[572,3251,3253],{"className":3252},[664],[572,3254,3256,3276],{"className":3255},[668,669],[572,3257,3259,3273],{"className":3258},[673],[572,3260,3262],{"className":3261,"style":678},[677],[572,3263,3264,3267],{"style":681},[572,3265],{"className":3266,"style":686},[685],[572,3268,3270],{"className":3269},[690,691,692,693],[572,3271,593],{"className":3272,"style":650},[648,649,693],[572,3274,701],{"className":3275},[700],[572,3277,3279],{"className":3278},[673],[572,3280,3282],{"className":3281,"style":708},[677],[572,3283],{},[572,3285,598],{"className":3286},[654],[572,3288,604],{"className":3289},[648,649],[572,3291,623],{"className":3292},[779],[572,3294],{"className":3295,"style":715},[714],[572,3297,898],{"className":3298},[719],[572,3300],{"className":3301,"style":715},[714],[572,3303,3305,3308,3311,3314,3317],{"className":3304},[639],[572,3306],{"className":3307,"style":1012},[643],[572,3309,2071],{"className":3310},[648],[572,3312],{"className":3313,"style":2164},[714],[572,3315,3211],{"className":3316},[2168],[572,3318],{"className":3319,"style":2164},[714],[572,3321,3323,3326,3329,3332,3335,3338],{"className":3322},[639],[572,3324],{"className":3325,"style":644},[643],[572,3327,598],{"className":3328},[654],[572,3330,604],{"className":3331},[648,649],[572,3333],{"className":3334,"style":2164},[714],[572,3336,1834],{"className":3337},[2168],[572,3339],{"className":3340,"style":2164},[714],[572,3342,3344,3347,3350,3353,3356,3359],{"className":3343},[639],[572,3345],{"className":3346,"style":644},[643],[572,3348,1840],{"className":3349},[648],[572,3351,623],{"className":3352},[779],[572,3354],{"className":3355,"style":2164},[714],[572,3357,2074],{"className":3358},[2168],[572,3360],{"className":3361,"style":2164},[714],[572,3363,3365,3368,3371,3374,3377],{"className":3364},[639],[572,3366],{"className":3367,"style":1012},[643],[572,3369,2071],{"className":3370},[648],[572,3372],{"className":3373,"style":715},[714],[572,3375,898],{"className":3376},[719],[572,3378],{"className":3379,"style":715},[714],[572,3381,3383,3386,3389],{"className":3382},[639],[572,3384],{"className":3385,"style":1012},[643],[572,3387,2071],{"className":3388},[648],[572,3390,604],{"className":3391},[648,649],[564,3393,3394,3395,3607,3608,3660],{},"Die Wendetangente geht hier durch den Ursprung. Die Differenz ",[572,3396,3398,3450],{"className":3397},[575],[572,3399,3401],{"className":3400},[579],[581,3402,3403],{"xmlns":583},[585,3404,3405,3447],{},[588,3406,3407,3409,3411,3413,3415,3417,3423,3425,3427,3429,3431,3433,3435,3437,3439,3441],{},[591,3408,612],{},[595,3410,598],{"stretchy":597},[591,3412,604],{},[595,3414,623],{"stretchy":597},[595,3416,1834],{},[600,3418,3419,3421],{},[591,3420,3196],{},[591,3422,593],{},[595,3424,598],{"stretchy":597},[591,3426,604],{},[595,3428,623],{"stretchy":597},[595,3430,898],{},[595,3432,1834],{},[595,3434,598],{"stretchy":597},[591,3436,604],{},[595,3438,1834],{},[900,3440,1840],{},[874,3442,3443,3445],{},[595,3444,623],{"stretchy":597},[900,3446,2071],{},[627,3448,3449],{"encoding":629},"f(x) - t_W(x) = -(x - 1)^3",[572,3451,3453,3480,3544,3568],{"className":3452,"ariaHidden":635},[634],[572,3454,3456,3459,3462,3465,3468,3471,3474,3477],{"className":3455},[639],[572,3457],{"className":3458,"style":644},[643],[572,3460,612],{"className":3461,"style":732},[648,649],[572,3463,598],{"className":3464},[654],[572,3466,604],{"className":3467},[648,649],[572,3469,623],{"className":3470},[779],[572,3472],{"className":3473,"style":2164},[714],[572,3475,1834],{"className":3476},[2168],[572,3478],{"className":3479,"style":2164},[714],[572,3481,3483,3486,3526,3529,3532,3535,3538,3541],{"className":3482},[639],[572,3484],{"className":3485,"style":644},[643],[572,3487,3489,3492],{"className":3488},[648],[572,3490,3196],{"className":3491},[648,649],[572,3493,3495],{"className":3494},[664],[572,3496,3498,3518],{"className":3497},[668,669],[572,3499,3501,3515],{"className":3500},[673],[572,3502,3504],{"className":3503,"style":678},[677],[572,3505,3506,3509],{"style":681},[572,3507],{"className":3508,"style":686},[685],[572,3510,3512],{"className":3511},[690,691,692,693],[572,3513,593],{"className":3514,"style":650},[648,649,693],[572,3516,701],{"className":3517},[700],[572,3519,3521],{"className":3520},[673],[572,3522,3524],{"className":3523,"style":708},[677],[572,3525],{},[572,3527,598],{"className":3528},[654],[572,3530,604],{"className":3531},[648,649],[572,3533,623],{"className":3534},[779],[572,3536],{"className":3537,"style":715},[714],[572,3539,898],{"className":3540},[719],[572,3542],{"className":3543,"style":715},[714],[572,3545,3547,3550,3553,3556,3559,3562,3565],{"className":3546},[639],[572,3548],{"className":3549,"style":644},[643],[572,3551,1834],{"className":3552},[648],[572,3554,598],{"className":3555},[654],[572,3557,604],{"className":3558},[648,649],[572,3560],{"className":3561,"style":2164},[714],[572,3563,1834],{"className":3564},[2168],[572,3566],{"className":3567,"style":2164},[714],[572,3569,3571,3575,3578],{"className":3570},[639],[572,3572],{"className":3573,"style":3574},[643],"height:1.0641em;vertical-align:-0.25em;",[572,3576,1840],{"className":3577},[648],[572,3579,3581,3584],{"className":3580},[779],[572,3582,623],{"className":3583},[779],[572,3585,3587],{"className":3586},[664],[572,3588,3590],{"className":3589},[668],[572,3591,3593],{"className":3592},[673],[572,3594,3596],{"className":3595,"style":2149},[677],[572,3597,3598,3601],{"style":937},[572,3599],{"className":3600,"style":686},[685],[572,3602,3604],{"className":3603},[690,691,692,693],[572,3605,2071],{"className":3606},[648,693]," wechselt bei ",[572,3609,3611,3629],{"className":3610},[575],[572,3612,3614],{"className":3613},[579],[581,3615,3616],{"xmlns":583},[585,3617,3618,3626],{},[588,3619,3620,3622,3624],{},[591,3621,604],{},[595,3623,898],{},[900,3625,1840],{},[627,3627,3628],{"encoding":629},"x = 1",[572,3630,3632,3651],{"className":3631,"ariaHidden":635},[634],[572,3633,3635,3639,3642,3645,3648],{"className":3634},[639],[572,3636],{"className":3637,"style":3638},[643],"height:0.4306em;",[572,3640,604],{"className":3641},[648,649],[572,3643],{"className":3644,"style":715},[714],[572,3646,898],{"className":3647},[719],[572,3649],{"className":3650,"style":715},[714],[572,3652,3654,3657],{"className":3653},[639],[572,3655],{"className":3656,"style":1012},[643],[572,3658,1840],{"className":3659},[648]," das Vorzeichen, der Graph durchsetzt die Tangente also wirklich.",[564,3662,3663,3664,3174],{},"Die Wendenormale hat die Steigung 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Die Wendetangente ist die x-Achse ",[572,4552,4554,4573],{"className":4553},[575],[572,4555,4557],{"className":4556},[579],[581,4558,4559],{"xmlns":583},[585,4560,4561,4570],{},[588,4562,4563,4566,4568],{},[591,4564,4565],{},"y",[595,4567,898],{},[900,4569,902],{},[627,4571,4572],{"encoding":629},"y = 0",[572,4574,4576,4596],{"className":4575,"ariaHidden":635},[634],[572,4577,4579,4583,4587,4590,4593],{"className":4578},[639],[572,4580],{"className":4581,"style":4582},[643],"height:0.625em;vertical-align:-0.1944em;",[572,4584,4565],{"className":4585,"style":4586},[648,649],"margin-right:0.0359em;",[572,4588],{"className":4589,"style":715},[714],[572,4591,898],{"className":4592},[719],[572,4594],{"className":4595,"style":715},[714],[572,4597,4599,4602],{"className":4598},[639],[572,4600],{"className":4601,"style":1012},[643],[572,4603,902],{"className":4604},[648],", der Ursprung ein Sattelpunkt.",[559,4607,4609],{"id":4608},"typische-fehler","Typische Fehler",[4611,4612,4613,5007,5123],"ul",{},[786,4614,4615,4616,4738,4739,4856,4857,4978,4979,1640],{},"Die Steigung mit ",[572,4617,4619,4651],{"className":4618},[575],[572,4620,4622],{"className":4621},[579],[581,4623,4624],{"xmlns":583},[585,4625,4626,4648],{},[588,4627,4628,4638,4640,4646],{},[874,4629,4630,4632],{},[591,4631,612],{},[588,4633,4634,4636],{},[595,4635,883],{"mathvariant":882},[595,4637,883],{"mathvariant":882},[595,4639,598],{"stretchy":597},[600,4641,4642,4644],{},[591,4643,604],{},[591,4645,593],{},[595,4647,623],{"stretchy":597},[627,4649,4650],{"encoding":629},"f''(x_W)",[572,4652,4654],{"className":4653,"ariaHidden":635},[634],[572,4655,4657,4660,4692,4695,4735],{"className":4656},[639],[572,4658],{"className":4659,"style":915},[643],[572,4661,4663,4666],{"className":4662},[648],[572,4664,612],{"className":4665,"style":732},[648,649],[572,4667,4669],{"className":4668},[664],[572,4670,4672],{"className":4671},[668],[572,4673,4675],{"className":4674},[673],[572,4676,4678],{"className":4677,"style":934},[677],[572,4679,4680,4683],{"style":937},[572,4681],{"className":4682,"style":686},[685],[572,4684,4686],{"className":4685},[690,691,692,693],[572,4687,4689],{"className":4688},[648,693],[572,4690,950],{"className":4691},[648,693],[572,4693,598],{"className":4694},[654],[572,4696,4698,4701],{"className":4697},[648],[572,4699,604],{"className":4700},[648,649],[572,4702,4704],{"className":4703},[664],[572,4705,4707,4727],{"className":4706},[668,669],[572,4708,4710,4724],{"className":4709},[673],[572,4711,4713],{"className":4712,"style":678},[677],[572,4714,4715,4718],{"style":681},[572,4716],{"className":4717,"style":686},[685],[572,4719,4721],{"className":4720},[690,691,692,693],[572,4722,593],{"className":4723,"style":650},[648,649,693],[572,4725,701],{"className":4726},[700],[572,4728,4730],{"className":4729},[673],[572,4731,4733],{"className":4732,"style":708},[677],[572,4734],{},[572,4736,623],{"className":4737},[779]," statt mit ",[572,4740,4742,4769],{"className":4741},[575],[572,4743,4745],{"className":4744},[579],[581,4746,4747],{"xmlns":583},[585,4748,4749,4767],{},[588,4750,4751,4757,4759,4765],{},[874,4752,4753,4755],{},[591,4754,612],{},[595,4756,883],{"mathvariant":882,"lspace":1381,"rspace":1381},[595,4758,598],{"stretchy":597},[600,4760,4761,4763],{},[591,4762,604],{},[591,4764,593],{},[595,4766,623],{"stretchy":597},[627,4768,1394],{"encoding":629},[572,4770,4772],{"className":4771,"ariaHidden":635},[634],[572,4773,4775,4778,4810,4813,4853],{"className":4774},[639],[572,4776],{"className":4777,"style":915},[643],[572,4779,4781,4784],{"className":4780},[648],[572,4782,612],{"className":4783,"style":732},[648,649],[572,4785,4787],{"className":4786},[664],[572,4788,4790],{"className":4789},[668],[572,4791,4793],{"className":4792},[673],[572,4794,4796],{"className":4795,"style":934},[677],[572,4797,4798,4801],{"style":937},[572,4799],{"className":4800,"style":686},[685],[572,4802,4804],{"className":4803},[690,691,692,693],[572,4805,4807],{"className":4806},[648,693],[572,4808,883],{"className":4809},[648,693],[572,4811,598],{"className":4812},[654],[572,4814,4816,4819],{"className":4815},[648],[572,4817,604],{"className":4818},[648,649],[572,4820,4822],{"className":4821},[664],[572,4823,4825,4845],{"className":4824},[668,669],[572,4826,4828,4842],{"className":4827},[673],[572,4829,4831],{"className":4830,"style":678},[677],[572,4832,4833,4836],{"style":681},[572,4834],{"className":4835,"style":686},[685],[572,4837,4839],{"className":4838},[690,691,692,693],[572,4840,593],{"className":4841,"style":650},[648,649,693],[572,4843,701],{"className":4844},[700],[572,4846,4848],{"className":4847},[673],[572,4849,4851],{"className":4850,"style":708},[677],[572,4852],{},[572,4854,623],{"className":4855},[779]," berechnen. ",[572,4858,4860,4891],{"className":4859},[575],[572,4861,4863],{"className":4862},[579],[581,4864,4865],{"xmlns":583},[585,4866,4867,4889],{},[588,4868,4869,4879,4881,4887],{},[874,4870,4871,4873],{},[591,4872,612],{},[588,4874,4875,4877],{},[595,4876,883],{"mathvariant":882},[595,4878,883],{"mathvariant":882},[595,4880,598],{"stretchy":597},[600,4882,4883,4885],{},[591,4884,604],{},[591,4886,593],{},[595,4888,623],{"stretchy":597},[627,4890,4650],{"encoding":629},[572,4892,4894],{"className":4893,"ariaHidden":635},[634],[572,4895,4897,4900,4932,4935,4975],{"className":4896},[639],[572,4898],{"className":4899,"style":915},[643],[572,4901,4903,4906],{"className":4902},[648],[572,4904,612],{"className":4905,"style":732},[648,649],[572,4907,4909],{"className":4908},[664],[572,4910,4912],{"className":4911},[668],[572,4913,4915],{"className":4914},[673],[572,4916,4918],{"className":4917,"style":934},[677],[572,4919,4920,4923],{"style":937},[572,4921],{"className":4922,"style":686},[685],[572,4924,4926],{"className":4925},[690,691,692,693],[572,4927,4929],{"className":4928},[648,693],[572,4930,950],{"className":4931},[648,693],[572,4933,598],{"className":4934},[654],[572,4936,4938,4941],{"className":4937},[648],[572,4939,604],{"className":4940},[648,649],[572,4942,4944],{"className":4943},[664],[572,4945,4947,4967],{"className":4946},[668,669],[572,4948,4950,4964],{"className":4949},[673],[572,4951,4953],{"className":4952,"style":678},[677],[572,4954,4955,4958],{"style":681},[572,4956],{"className":4957,"style":686},[685],[572,4959,4961],{"className":4960},[690,691,692,693],[572,4962,593],{"className":4963,"style":650},[648,649,693],[572,4965,701],{"className":4966},[700],[572,4968,4970],{"className":4969},[673],[572,4971,4973],{"className":4972,"style":708},[677],[572,4974],{},[572,4976,623],{"className":4977},[779]," ist im Wendepunkt immer ",[572,4980,4982,4995],{"className":4981},[575],[572,4983,4985],{"className":4984},[579],[581,4986,4987],{"xmlns":583},[585,4988,4989,4993],{},[588,4990,4991],{},[900,4992,902],{},[627,4994,902],{"encoding":629},[572,4996,4998],{"className":4997,"ariaHidden":635},[634],[572,4999,5001,5004],{"className":5000},[639],[572,5002],{"className":5003,"style":1012},[643],[572,5005,902],{"className":5006},[648],[786,5008,5009,5010,5094,5095,1482],{},"Den y-Wert ",[572,5011,5013,5036],{"className":5012},[575],[572,5014,5016],{"className":5015},[579],[581,5017,5018],{"xmlns":583},[585,5019,5020,5034],{},[588,5021,5022,5024,5026,5032],{},[591,5023,612],{},[595,5025,598],{"stretchy":597},[600,5027,5028,5030],{},[591,5029,604],{},[591,5031,593],{},[595,5033,623],{"stretchy":597},[627,5035,1303],{"encoding":629},[572,5037,5039],{"className":5038,"ariaHidden":635},[634],[572,5040,5042,5045,5048,5051,5091],{"className":5041},[639],[572,5043],{"className":5044,"style":644},[643],[572,5046,612],{"className":5047,"style":732},[648,649],[572,5049,598],{"className":5050},[654],[572,5052,5054,5057],{"className":5053},[648],[572,5055,604],{"className":5056},[648,649],[572,5058,5060],{"className":5059},[664],[572,5061,5063,5083],{"className":5062},[668,669],[572,5064,5066,5080],{"className":5065},[673],[572,5067,5069],{"className":5068,"style":678},[677],[572,5070,5071,5074],{"style":681},[572,5072],{"className":5073,"style":686},[685],[572,5075,5077],{"className":5076},[690,691,692,693],[572,5078,593],{"className":5079,"style":650},[648,649,693],[572,5081,701],{"className":5082},[700],[572,5084,5086],{"className":5085},[673],[572,5087,5089],{"className":5088,"style":708},[677],[572,5090],{},[572,5092,623],{"className":5093},[779]," vergessen oder in einer Ableitung statt in ",[572,5096,5098,5111],{"className":5097},[575],[572,5099,5101],{"className":5100},[579],[581,5102,5103],{"xmlns":583},[585,5104,5105,5109],{},[588,5106,5107],{},[591,5108,612],{},[627,5110,612],{"encoding":629},[572,5112,5114],{"className":5113,"ariaHidden":635},[634],[572,5115,5117,5120],{"className":5116},[639],[572,5118],{"className":5119,"style":1171},[643],[572,5121,612],{"className":5122,"style":732},[648,649],[786,5124,5125],{},"Bei der Wendenormale nur das Vorzeichen der Steigung umdrehen. Richtig ist der negative Kehrwert.",{"title":5127,"searchDepth":5128,"depth":5128,"links":5129},"",2,[5130,5131,5132],{"id":561,"depth":5128,"text":562},{"id":2037,"depth":5128,"text":2038},{"id":4608,"depth":5128,"text":4609},[5134,5138,5140,5142,5145,5148,5151],{"lhs":5135,"rhs":902,"where":5136},"-6*x + 6",{"x":5137},1,{"lhs":5139,"rhs":2071},"-(1^3) + 3*1^2 + 1",{"lhs":5141,"rhs":2071},"-3*1^2 + 6*1",{"lhs":5143,"rhs":5144},"3*(x - 1) + 3","3*x",{"lhs":5146,"rhs":5147},"-x^3 + 3*x^2 + 1 - 3*x","-(x - 1)^3",{"lhs":5149,"rhs":5150},"-1\u002F3*(x - 1) + 3","-x\u002F3 + 10\u002F3",{"lhs":5152,"rhs":902},"3*0^2*(x - 0) + 0^3","x_W \\text{ Wendestelle von } f,\\ f \\text{ differenzierbar in } x_W","\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> \u003Cspan class=\"katex\">Wendestelle von\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f,\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\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f\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\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">differenzierbar in\u003C\u002Fspan> \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\" 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