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Ist ",[571,798,800,813],{"className":799},[574],[571,801,803],{"className":802},[578],[580,804,805],{"xmlns":582},[584,806,807,811],{},[587,808,809],{},[590,810,592],{},[617,812,592],{"encoding":619},[571,814,816],{"className":815,"ariaHidden":625},[624],[571,817,819,822],{"className":818},[629],[571,820],{"className":821,"style":760},[633],[571,823,592],{"className":824,"style":640},[638,639]," konstant, gilt ",[571,827,829,855],{"className":828},[574],[571,830,832],{"className":831},[578],[580,833,834],{"xmlns":582},[584,835,836,852],{},[587,837,838,848,850],{},[839,840,841,843],"msup",{},[590,842,592],{},[594,844,847],{"mathvariant":845,"lspace":846,"rspace":846},"normal","0em","′",[594,849,606],{},[778,851,780],{},[617,853,854],{"encoding":619},"f' = 0",[571,856,858,918],{"className":857,"ariaHidden":625},[624],[571,859,861,865,909,912,915],{"className":860},[629],[571,862],{"className":863,"style":864},[633],"height:0.9463em;vertical-align:-0.1944em;",[571,866,868,871],{"className":867},[638],[571,869,592],{"className":870,"style":640},[638,639],[571,872,875],{"className":873},[874],"msupsub",[571,876,879],{"className":877},[878],"vlist-t",[571,880,883],{"className":881},[882],"vlist-r",[571,884,888],{"className":885,"style":887},[886],"vlist","height:0.7519em;",[571,889,891,896],{"style":890},"top:-3.063em;margin-right:0.05em;",[571,892],{"className":893,"style":895},[894],"pstrut","height:2.7em;",[571,897,903],{"className":898},[899,900,901,902],"sizing","reset-size6","size3","mtight",[571,904,906],{"className":905},[638,902],[571,907,847],{"className":908},[638,902],[571,910],{"className":911,"style":656},[655],[571,913,606],{"className":914},[660],[571,916],{"className":917,"style":656},[655],[571,919,921,924],{"className":920},[629],[571,922],{"className":923,"style":792},[633],[571,925,780],{"className":926},[638]," sogar überall.",[563,929,930,931,934,935,963,964,1026,1027,1088,1089,1117,1118,1149,1150,1206],{},"Wichtige Anwendung: ",[567,932,933],{},"Nullstellen zählen."," Zwischen zwei Nullstellen von ",[571,936,938,951],{"className":937},[574],[571,939,941],{"className":940},[578],[580,942,943],{"xmlns":582},[584,944,945,949],{},[587,946,947],{},[590,948,592],{},[617,950,592],{"encoding":619},[571,952,954],{"className":953,"ariaHidden":625},[624],[571,955,957,960],{"className":956},[629],[571,958],{"className":959,"style":760},[633],[571,961,592],{"className":962,"style":640},[638,639]," liegt nach Rolle eine Nullstelle von ",[571,965,967,985],{"className":966},[574],[571,968,970],{"className":969},[578],[580,971,972],{"xmlns":582},[584,973,974,982],{},[587,975,976],{},[839,977,978,980],{},[590,979,592],{},[594,981,847],{"mathvariant":845,"lspace":846,"rspace":846},[617,983,984],{"encoding":619},"f'",[571,986,988],{"className":987,"ariaHidden":625},[624],[571,989,991,994],{"className":990},[629],[571,992],{"className":993,"style":864},[633],[571,995,997,1000],{"className":996},[638],[571,998,592],{"className":999,"style":640},[638,639],[571,1001,1003],{"className":1002},[874],[571,1004,1006],{"className":1005},[878],[571,1007,1009],{"className":1008},[882],[571,1010,1012],{"className":1011,"style":887},[886],[571,1013,1014,1017],{"style":890},[571,1015],{"className":1016,"style":895},[894],[571,1018,1020],{"className":1019},[899,900,901,902],[571,1021,1023],{"className":1022},[638,902],[571,1024,847],{"className":1025},[638,902],". Hat ",[571,1028,1030,1047],{"className":1029},[574],[571,1031,1033],{"className":1032},[578],[580,1034,1035],{"xmlns":582},[584,1036,1037,1045],{},[587,1038,1039],{},[839,1040,1041,1043],{},[590,1042,592],{},[594,1044,847],{"mathvariant":845,"lspace":846,"rspace":846},[617,1046,984],{"encoding":619},[571,1048,1050],{"className":1049,"ariaHidden":625},[624],[571,1051,1053,1056],{"className":1052},[629],[571,1054],{"className":1055,"style":864},[633],[571,1057,1059,1062],{"className":1058},[638],[571,1060,592],{"className":1061,"style":640},[638,639],[571,1063,1065],{"className":1064},[874],[571,1066,1068],{"className":1067},[878],[571,1069,1071],{"className":1070},[882],[571,1072,1074],{"className":1073,"style":887},[886],[571,1075,1076,1079],{"style":890},[571,1077],{"className":1078,"style":895},[894],[571,1080,1082],{"className":1081},[899,900,901,902],[571,1083,1085],{"className":1084},[638,902],[571,1086,847],{"className":1087},[638,902]," also keine Nullstelle, hat ",[571,1090,1092,1105],{"className":1091},[574],[571,1093,1095],{"className":1094},[578],[580,1096,1097],{"xmlns":582},[584,1098,1099,1103],{},[587,1100,1101],{},[590,1102,592],{},[617,1104,592],{"encoding":619},[571,1106,1108],{"className":1107,"ariaHidden":625},[624],[571,1109,1111,1114],{"className":1110},[629],[571,1112],{"className":1113,"style":760},[633],[571,1115,592],{"className":1116,"style":640},[638,639]," höchstens eine. Allgemein hat ein Polynom mit ",[571,1119,1121,1135],{"className":1120},[574],[571,1122,1124],{"className":1123},[578],[580,1125,1126],{"xmlns":582},[584,1127,1128,1133],{},[587,1129,1130],{},[590,1131,1132],{},"k",[617,1134,1132],{"encoding":619},[571,1136,1138],{"className":1137,"ariaHidden":625},[624],[571,1139,1141,1145],{"className":1140},[629],[571,1142],{"className":1143,"style":1144},[633],"height:0.6944em;",[571,1146,1132],{"className":1147,"style":1148},[638,639],"margin-right:0.0315em;"," verschiedenen reellen Nullstellen eine Ableitung mit mindestens ",[571,1151,1153,1173],{"className":1152},[574],[571,1154,1156],{"className":1155},[578],[580,1157,1158],{"xmlns":582},[584,1159,1160,1170],{},[587,1161,1162,1164,1167],{},[590,1163,1132],{},[594,1165,1166],{},"−",[778,1168,1169],{},"1",[617,1171,1172],{"encoding":619},"k - 1",[571,1174,1176,1197],{"className":1175,"ariaHidden":625},[624],[571,1177,1179,1183,1186,1190,1194],{"className":1178},[629],[571,1180],{"className":1181,"style":1182},[633],"height:0.7778em;vertical-align:-0.0833em;",[571,1184,1132],{"className":1185,"style":1148},[638,639],[571,1187],{"className":1188,"style":1189},[655],"margin-right:0.2222em;",[571,1191,1166],{"className":1192},[1193],"mbin",[571,1195],{"className":1196,"style":1189},[655],[571,1198,1200,1203],{"className":1199},[629],[571,1201],{"className":1202,"style":792},[633],[571,1204,1169],{"className":1205},[638]," Nullstellen.",[558,1208,1210],{"id":1209},"beispiele","Beispiele",[563,1212,1213,1365,1366,1423,1424,1527,1528,1679,1680,1731],{},[571,1214,1216,1258],{"className":1215},[574],[571,1217,1219],{"className":1218},[578],[580,1220,1221],{"xmlns":582},[584,1222,1223,1255],{},[587,1224,1225,1227,1229,1232,1234,1236,1243,1245,1248,1250,1253],{},[590,1226,592],{},[594,1228,597],{"stretchy":596},[590,1230,1231],{},"x",[594,1233,603],{"stretchy":596},[594,1235,606],{},[839,1237,1238,1240],{},[590,1239,1231],{},[778,1241,1242],{},"2",[594,1244,1166],{},[778,1246,1247],{},"4",[590,1249,1231],{},[594,1251,1252],{},"+",[778,1254,1169],{},[617,1256,1257],{"encoding":619},"f(x) = x^2 - 4x + 1",[571,1259,1261,1288,1334,1356],{"className":1260,"ariaHidden":625},[624],[571,1262,1264,1267,1270,1273,1276,1279,1282,1285],{"className":1263},[629],[571,1265],{"className":1266,"style":634},[633],[571,1268,592],{"className":1269,"style":640},[638,639],[571,1271,597],{"className":1272},[644],[571,1274,1231],{"className":1275},[638,639],[571,1277,603],{"className":1278},[651],[571,1280],{"className":1281,"style":656},[655],[571,1283,606],{"className":1284},[660],[571,1286],{"className":1287,"style":656},[655],[571,1289,1291,1295,1325,1328,1331],{"className":1290},[629],[571,1292],{"className":1293,"style":1294},[633],"height:0.8974em;vertical-align:-0.0833em;",[571,1296,1298,1301],{"className":1297},[638],[571,1299,1231],{"className":1300},[638,639],[571,1302,1304],{"className":1303},[874],[571,1305,1307],{"className":1306},[878],[571,1308,1310],{"className":1309},[882],[571,1311,1314],{"className":1312,"style":1313},[886],"height:0.8141em;",[571,1315,1316,1319],{"style":890},[571,1317],{"className":1318,"style":895},[894],[571,1320,1322],{"className":1321},[899,900,901,902],[571,1323,1242],{"className":1324},[638,902],[571,1326],{"className":1327,"style":1189},[655],[571,1329,1166],{"className":1330},[1193],[571,1332],{"className":1333,"style":1189},[655],[571,1335,1337,1341,1344,1347,1350,1353],{"className":1336},[629],[571,1338],{"className":1339,"style":1340},[633],"height:0.7278em;vertical-align:-0.0833em;",[571,1342,1247],{"className":1343},[638],[571,1345,1231],{"className":1346},[638,639],[571,1348],{"className":1349,"style":1189},[655],[571,1351,1252],{"className":1352},[1193],[571,1354],{"className":1355,"style":1189},[655],[571,1357,1359,1362],{"className":1358},[629],[571,1360],{"className":1361,"style":792},[633],[571,1363,1169],{"className":1364},[638]," auf ",[571,1367,1369,1394],{"className":1368},[574],[571,1370,1372],{"className":1371},[578],[580,1373,1374],{"xmlns":582},[584,1375,1376,1391],{},[587,1377,1378,1381,1383,1386,1388],{},[594,1379,1380],{"stretchy":596},"[",[778,1382,780],{},[594,1384,1385],{"separator":625},",",[778,1387,1247],{},[594,1389,1390],{"stretchy":596},"]",[617,1392,1393],{"encoding":619},"[0, 4]",[571,1395,1397],{"className":1396,"ariaHidden":625},[624],[571,1398,1400,1403,1406,1409,1413,1417,1420],{"className":1399},[629],[571,1401],{"className":1402,"style":634},[633],[571,1404,1380],{"className":1405},[644],[571,1407,780],{"className":1408},[638],[571,1410,1385],{"className":1411},[1412],"mpunct",[571,1414],{"className":1415,"style":1416},[655],"margin-right:0.1667em;",[571,1418,1247],{"className":1419},[638],[571,1421,1390],{"className":1422},[651],": Es gilt ",[571,1425,1427,1461],{"className":1426},[574],[571,1428,1430],{"className":1429},[578],[580,1431,1432],{"xmlns":582},[584,1433,1434,1458],{},[587,1435,1436,1438,1440,1442,1444,1446,1448,1450,1452,1454,1456],{},[590,1437,592],{},[594,1439,597],{"stretchy":596},[778,1441,780],{},[594,1443,603],{"stretchy":596},[594,1445,606],{},[590,1447,592],{},[594,1449,597],{"stretchy":596},[778,1451,1247],{},[594,1453,603],{"stretchy":596},[594,1455,606],{},[778,1457,1169],{},[617,1459,1460],{"encoding":619},"f(0) = f(4) = 1",[571,1462,1464,1491,1518],{"className":1463,"ariaHidden":625},[624],[571,1465,1467,1470,1473,1476,1479,1482,1485,1488],{"className":1466},[629],[571,1468],{"className":1469,"style":634},[633],[571,1471,592],{"className":1472,"style":640},[638,639],[571,1474,597],{"className":1475},[644],[571,1477,780],{"className":1478},[638],[571,1480,603],{"className":1481},[651],[571,1483],{"className":1484,"style":656},[655],[571,1486,606],{"className":1487},[660],[571,1489],{"className":1490,"style":656},[655],[571,1492,1494,1497,1500,1503,1506,1509,1512,1515],{"className":1493},[629],[571,1495],{"className":1496,"style":634},[633],[571,1498,592],{"className":1499,"style":640},[638,639],[571,1501,597],{"className":1502},[644],[571,1504,1247],{"className":1505},[638],[571,1507,603],{"className":1508},[651],[571,1510],{"className":1511,"style":656},[655],[571,1513,606],{"className":1514},[660],[571,1516],{"className":1517,"style":656},[655],[571,1519,1521,1524],{"className":1520},[629],[571,1522],{"className":1523,"style":792},[633],[571,1525,1169],{"className":1526},[638],". Aus ",[571,1529,1531,1570],{"className":1530},[574],[571,1532,1534],{"className":1533},[578],[580,1535,1536],{"xmlns":582},[584,1537,1538,1567],{},[587,1539,1540,1546,1548,1551,1553,1555,1557,1559,1561,1563,1565],{},[839,1541,1542,1544],{},[590,1543,592],{},[594,1545,847],{"mathvariant":845,"lspace":846,"rspace":846},[594,1547,597],{"stretchy":596},[590,1549,1550],{},"ξ",[594,1552,603],{"stretchy":596},[594,1554,606],{},[778,1556,1242],{},[590,1558,1550],{},[594,1560,1166],{},[778,1562,1247],{},[594,1564,606],{},[778,1566,780],{},[617,1568,1569],{"encoding":619},"f'(\\xi) = 2\\xi - 4 = 0",[571,1571,1573,1631,1652,1670],{"className":1572,"ariaHidden":625},[624],[571,1574,1576,1580,1612,1615,1619,1622,1625,1628],{"className":1575},[629],[571,1577],{"className":1578,"style":1579},[633],"height:1.0019em;vertical-align:-0.25em;",[571,1581,1583,1586],{"className":1582},[638],[571,1584,592],{"className":1585,"style":640},[638,639],[571,1587,1589],{"className":1588},[874],[571,1590,1592],{"className":1591},[878],[571,1593,1595],{"className":1594},[882],[571,1596,1598],{"className":1597,"style":887},[886],[571,1599,1600,1603],{"style":890},[571,1601],{"className":1602,"style":895},[894],[571,1604,1606],{"className":1605},[899,900,901,902],[571,1607,1609],{"className":1608},[638,902],[571,1610,847],{"className":1611},[638,902],[571,1613,597],{"className":1614},[644],[571,1616,1550],{"className":1617,"style":1618},[638,639],"margin-right:0.046em;",[571,1620,603],{"className":1621},[651],[571,1623],{"className":1624,"style":656},[655],[571,1626,606],{"className":1627},[660],[571,1629],{"className":1630,"style":656},[655],[571,1632,1634,1637,1640,1643,1646,1649],{"className":1633},[629],[571,1635],{"className":1636,"style":760},[633],[571,1638,1242],{"className":1639},[638],[571,1641,1550],{"className":1642,"style":1618},[638,639],[571,1644],{"className":1645,"style":1189},[655],[571,1647,1166],{"className":1648},[1193],[571,1650],{"className":1651,"style":1189},[655],[571,1653,1655,1658,1661,1664,1667],{"className":1654},[629],[571,1656],{"className":1657,"style":792},[633],[571,1659,1247],{"className":1660},[638],[571,1662],{"className":1663,"style":656},[655],[571,1665,606],{"className":1666},[660],[571,1668],{"className":1669,"style":656},[655],[571,1671,1673,1676],{"className":1672},[629],[571,1674],{"className":1675,"style":792},[633],[571,1677,780],{"className":1678},[638]," folgt ",[571,1681,1683,1701],{"className":1682},[574],[571,1684,1686],{"className":1685},[578],[580,1687,1688],{"xmlns":582},[584,1689,1690,1698],{},[587,1691,1692,1694,1696],{},[590,1693,1550],{},[594,1695,606],{},[778,1697,1242],{},[617,1699,1700],{"encoding":619},"\\xi = 2",[571,1702,1704,1722],{"className":1703,"ariaHidden":625},[624],[571,1705,1707,1710,1713,1716,1719],{"className":1706},[629],[571,1708],{"className":1709,"style":760},[633],[571,1711,1550],{"className":1712,"style":1618},[638,639],[571,1714],{"className":1715,"style":656},[655],[571,1717,606],{"className":1718},[660],[571,1720],{"className":1721,"style":656},[655],[571,1723,1725,1728],{"className":1724},[629],[571,1726],{"className":1727,"style":792},[633],[571,1729,1242],{"className":1730},[638],", der Scheitelpunkt.",[563,1733,1734,1365,1854,1423,1911,1527,2019,1679,2128,2372],{},[571,1735,1737,1770],{"className":1736},[574],[571,1738,1740],{"className":1739},[578],[580,1741,1742],{"xmlns":582},[584,1743,1744,1767],{},[587,1745,1746,1748,1750,1752,1754,1756,1763,1765],{},[590,1747,592],{},[594,1749,597],{"stretchy":596},[590,1751,1231],{},[594,1753,603],{"stretchy":596},[594,1755,606],{},[839,1757,1758,1760],{},[590,1759,1231],{},[778,1761,1762],{},"3",[594,1764,1166],{},[590,1766,1231],{},[617,1768,1769],{"encoding":619},"f(x) = x^3 - x",[571,1771,1773,1800,1844],{"className":1772,"ariaHidden":625},[624],[571,1774,1776,1779,1782,1785,1788,1791,1794,1797],{"className":1775},[629],[571,1777],{"className":1778,"style":634},[633],[571,1780,592],{"className":1781,"style":640},[638,639],[571,1783,597],{"className":1784},[644],[571,1786,1231],{"className":1787},[638,639],[571,1789,603],{"className":1790},[651],[571,1792],{"className":1793,"style":656},[655],[571,1795,606],{"className":1796},[660],[571,1798],{"className":1799,"style":656},[655],[571,1801,1803,1806,1835,1838,1841],{"className":1802},[629],[571,1804],{"className":1805,"style":1294},[633],[571,1807,1809,1812],{"className":1808},[638],[571,1810,1231],{"className":1811},[638,639],[571,1813,1815],{"className":1814},[874],[571,1816,1818],{"className":1817},[878],[571,1819,1821],{"className":1820},[882],[571,1822,1824],{"className":1823,"style":1313},[886],[571,1825,1826,1829],{"style":890},[571,1827],{"className":1828,"style":895},[894],[571,1830,1832],{"className":1831},[899,900,901,902],[571,1833,1762],{"className":1834},[638,902],[571,1836],{"className":1837,"style":1189},[655],[571,1839,1166],{"className":1840},[1193],[571,1842],{"className":1843,"style":1189},[655],[571,1845,1847,1851],{"className":1846},[629],[571,1848],{"className":1849,"style":1850},[633],"height:0.4306em;",[571,1852,1231],{"className":1853},[638,639],[571,1855,1857,1881],{"className":1856},[574],[571,1858,1860],{"className":1859},[578],[580,1861,1862],{"xmlns":582},[584,1863,1864,1878],{},[587,1865,1866,1868,1870,1872,1874,1876],{},[594,1867,1380],{"stretchy":596},[594,1869,1166],{},[778,1871,1169],{},[594,1873,1385],{"separator":625},[778,1875,1169],{},[594,1877,1390],{"stretchy":596},[617,1879,1880],{"encoding":619},"[-1, 1]",[571,1882,1884],{"className":1883,"ariaHidden":625},[624],[571,1885,1887,1890,1893,1896,1899,1902,1905,1908],{"className":1886},[629],[571,1888],{"className":1889,"style":634},[633],[571,1891,1380],{"className":1892},[644],[571,1894,1166],{"className":1895},[638],[571,1897,1169],{"className":1898},[638],[571,1900,1385],{"className":1901},[1412],[571,1903],{"className":1904,"style":1416},[655],[571,1906,1169],{"className":1907},[638],[571,1909,1390],{"className":1910},[651],[571,1912,1914,1950],{"className":1913},[574],[571,1915,1917],{"className":1916},[578],[580,1918,1919],{"xmlns":582},[584,1920,1921,1947],{},[587,1922,1923,1925,1927,1929,1931,1933,1935,1937,1939,1941,1943,1945],{},[590,1924,592],{},[594,1926,597],{"stretchy":596},[594,1928,1166],{},[778,1930,1169],{},[594,1932,603],{"stretchy":596},[594,1934,606],{},[590,1936,592],{},[594,1938,597],{"stretchy":596},[778,1940,1169],{},[594,1942,603],{"stretchy":596},[594,1944,606],{},[778,1946,780],{},[617,1948,1949],{"encoding":619},"f(-1) = f(1) = 0",[571,1951,1953,1983,2010],{"className":1952,"ariaHidden":625},[624],[571,1954,1956,1959,1962,1965,1968,1971,1974,1977,1980],{"className":1955},[629],[571,1957],{"className":1958,"style":634},[633],[571,1960,592],{"className":1961,"style":640},[638,639],[571,1963,597],{"className":1964},[644],[571,1966,1166],{"className":1967},[638],[571,1969,1169],{"className":1970},[638],[571,1972,603],{"className":1973},[651],[571,1975],{"className":1976,"style":656},[655],[571,1978,606],{"className":1979},[660],[571,1981],{"className":1982,"style":656},[655],[571,1984,1986,1989,1992,1995,1998,2001,2004,2007],{"className":1985},[629],[571,1987],{"className":1988,"style":634},[633],[571,1990,592],{"className":1991,"style":640},[638,639],[571,1993,597],{"className":1994},[644],[571,1996,1169],{"className":1997},[638],[571,1999,603],{"className":2000},[651],[571,2002],{"className":2003,"style":656},[655],[571,2005,606],{"className":2006},[660],[571,2008],{"className":2009,"style":656},[655],[571,2011,2013,2016],{"className":2012},[629],[571,2014],{"className":2015,"style":792},[633],[571,2017,780],{"className":2018},[638],[571,2020,2022,2050],{"className":2021},[574],[571,2023,2025],{"className":2024},[578],[580,2026,2027],{"xmlns":582},[584,2028,2029,2047],{},[587,2030,2031,2033,2039,2041,2043,2045],{},[778,2032,1762],{},[839,2034,2035,2037],{},[590,2036,1550],{},[778,2038,1242],{},[594,2040,1166],{},[778,2042,1169],{},[594,2044,606],{},[778,2046,780],{},[617,2048,2049],{"encoding":619},"3\\xi^2 - 1 = 0",[571,2051,2053,2101,2119],{"className":2052,"ariaHidden":625},[624],[571,2054,2056,2060,2063,2092,2095,2098],{"className":2055},[629],[571,2057],{"className":2058,"style":2059},[633],"height:1.0085em;vertical-align:-0.1944em;",[571,2061,1762],{"className":2062},[638],[571,2064,2066,2069],{"className":2065},[638],[571,2067,1550],{"className":2068,"style":1618},[638,639],[571,2070,2072],{"className":2071},[874],[571,2073,2075],{"className":2074},[878],[571,2076,2078],{"className":2077},[882],[571,2079,2081],{"className":2080,"style":1313},[886],[571,2082,2083,2086],{"style":890},[571,2084],{"className":2085,"style":895},[894],[571,2087,2089],{"className":2088},[899,900,901,902],[571,2090,1242],{"className":2091},[638,902],[571,2093],{"className":2094,"style":1189},[655],[571,2096,1166],{"className":2097},[1193],[571,2099],{"className":2100,"style":1189},[655],[571,2102,2104,2107,2110,2113,2116],{"className":2103},[629],[571,2105],{"className":2106,"style":792},[633],[571,2108,1169],{"className":2109},[638],[571,2111],{"className":2112,"style":656},[655],[571,2114,606],{"className":2115},[660],[571,2117],{"className":2118,"style":656},[655],[571,2120,2122,2125],{"className":2121},[629],[571,2123],{"className":2124,"style":792},[633],[571,2126,780],{"className":2127},[638],[571,2129,2131,2168],{"className":2130},[574],[571,2132,2134],{"className":2133},[578],[580,2135,2136],{"xmlns":582},[584,2137,2138,2165],{},[587,2139,2140,2142,2144,2147,2157,2160,2162],{},[590,2141,1550],{},[594,2143,606],{},[594,2145,2146],{},"±",[2148,2149,2150,2152],"mfrac",{},[778,2151,1169],{},[2153,2154,2155],"msqrt",{},[778,2156,1762],{},[594,2158,2159],{},"≈",[594,2161,2146],{},[778,2163,2164],{},"0,577",[617,2166,2167],{"encoding":619},"\\xi = \\pm\\frac{1}{\\sqrt{3}} \\approx \\pm 0{,}577",[571,2169,2171,2189,2349],{"className":2170,"ariaHidden":625},[624],[571,2172,2174,2177,2180,2183,2186],{"className":2173},[629],[571,2175],{"className":2176,"style":760},[633],[571,2178,1550],{"className":2179,"style":1618},[638,639],[571,2181],{"className":2182,"style":656},[655],[571,2184,606],{"className":2185},[660],[571,2187],{"className":2188,"style":656},[655],[571,2190,2192,2196,2199,2340,2343,2346],{"className":2191},[629],[571,2193],{"className":2194,"style":2195},[633],"height:1.3831em;vertical-align:-0.538em;",[571,2197,2146],{"className":2198},[638],[571,2200,2202,2206,2337],{"className":2201},[638],[571,2203],{"className":2204},[644,2205],"nulldelimiter",[571,2207,2209],{"className":2208},[2148],[571,2210,2213,2328],{"className":2211},[878,2212],"vlist-t2",[571,2214,2216,2325],{"className":2215},[882],[571,2217,2220,2299,2310],{"className":2218,"style":2219},[886],"height:0.8451em;",[571,2221,2223,2227],{"style":2222},"top:-2.551em;",[571,2224],{"className":2225,"style":2226},[894],"height:3em;",[571,2228,2230],{"className":2229},[899,900,901,902],[571,2231,2233],{"className":2232},[638,902],[571,2234,2237],{"className":2235},[638,2236,902],"sqrt",[571,2238,2240,2290],{"className":2239},[878,2212],[571,2241,2243,2285],{"className":2242},[882],[571,2244,2247,2262],{"className":2245,"style":2246},[886],"height:0.9128em;",[571,2248,2252,2255],{"className":2249,"style":2251},[2250],"svg-align","top:-3em;",[571,2253],{"className":2254,"style":2226},[894],[571,2256,2259],{"className":2257,"style":2258},[638,902],"padding-left:0.833em;",[571,2260,1762],{"className":2261},[638,902],[571,2263,2265,2268],{"style":2264},"top:-2.8728em;",[571,2266],{"className":2267,"style":2226},[894],[571,2269,2273],{"className":2270,"style":2272},[2271,902],"hide-tail","min-width:0.853em;height:1.08em;",[2274,2275,2281],"svg",{"xmlns":2276,"width":2277,"height":2278,"viewBox":2279,"preserveAspectRatio":2280},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[2282,2283],"path",{"d":2284},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[571,2286,2289],{"className":2287},[2288],"vlist-s","​",[571,2291,2293],{"className":2292},[882],[571,2294,2297],{"className":2295,"style":2296},[886],"height:0.1272em;",[571,2298],{},[571,2300,2302,2305],{"style":2301},"top:-3.23em;",[571,2303],{"className":2304,"style":2226},[894],[571,2306],{"className":2307,"style":2309},[2308],"frac-line","border-bottom-width:0.04em;",[571,2311,2313,2316],{"style":2312},"top:-3.394em;",[571,2314],{"className":2315,"style":2226},[894],[571,2317,2319],{"className":2318},[899,900,901,902],[571,2320,2322],{"className":2321},[638,902],[571,2323,1169],{"className":2324},[638,902],[571,2326,2289],{"className":2327},[2288],[571,2329,2331],{"className":2330},[882],[571,2332,2335],{"className":2333,"style":2334},[886],"height:0.538em;",[571,2336],{},[571,2338],{"className":2339},[651,2205],[571,2341],{"className":2342,"style":656},[655],[571,2344,2159],{"className":2345},[660],[571,2347],{"className":2348,"style":656},[655],[571,2350,2352,2356,2359,2362,2368],{"className":2351},[629],[571,2353],{"className":2354,"style":2355},[633],"height:0.8389em;vertical-align:-0.1944em;",[571,2357,2146],{"className":2358},[638],[571,2360,780],{"className":2361},[638],[571,2363,2365],{"className":2364},[638],[571,2366,1385],{"className":2367},[1412],[571,2369,2371],{"className":2370},[638],"577",". Hier gibt es also zwei passende Stellen.",[563,2374,2375,2516,2517,2545,2546,2702,2703,686],{},[571,2376,2378,2414],{"className":2377},[574],[571,2379,2381],{"className":2380},[578],[580,2382,2383],{"xmlns":582},[584,2384,2385,2411],{},[587,2386,2387,2389,2391,2393,2395,2397,2403,2405,2407,2409],{},[590,2388,592],{},[594,2390,597],{"stretchy":596},[590,2392,1231],{},[594,2394,603],{"stretchy":596},[594,2396,606],{},[839,2398,2399,2401],{},[590,2400,1231],{},[778,2402,1762],{},[594,2404,1252],{},[590,2406,1231],{},[594,2408,1166],{},[778,2410,1169],{},[617,2412,2413],{"encoding":619},"f(x) = x^3 + x - 1",[571,2415,2417,2444,2488,2507],{"className":2416,"ariaHidden":625},[624],[571,2418,2420,2423,2426,2429,2432,2435,2438,2441],{"className":2419},[629],[571,2421],{"className":2422,"style":634},[633],[571,2424,592],{"className":2425,"style":640},[638,639],[571,2427,597],{"className":2428},[644],[571,2430,1231],{"className":2431},[638,639],[571,2433,603],{"className":2434},[651],[571,2436],{"className":2437,"style":656},[655],[571,2439,606],{"className":2440},[660],[571,2442],{"className":2443,"style":656},[655],[571,2445,2447,2450,2479,2482,2485],{"className":2446},[629],[571,2448],{"className":2449,"style":1294},[633],[571,2451,2453,2456],{"className":2452},[638],[571,2454,1231],{"className":2455},[638,639],[571,2457,2459],{"className":2458},[874],[571,2460,2462],{"className":2461},[878],[571,2463,2465],{"className":2464},[882],[571,2466,2468],{"className":2467,"style":1313},[886],[571,2469,2470,2473],{"style":890},[571,2471],{"className":2472,"style":895},[894],[571,2474,2476],{"className":2475},[899,900,901,902],[571,2477,1762],{"className":2478},[638,902],[571,2480],{"className":2481,"style":1189},[655],[571,2483,1252],{"className":2484},[1193],[571,2486],{"className":2487,"style":1189},[655],[571,2489,2491,2495,2498,2501,2504],{"className":2490},[629],[571,2492],{"className":2493,"style":2494},[633],"height:0.6667em;vertical-align:-0.0833em;",[571,2496,1231],{"className":2497},[638,639],[571,2499],{"className":2500,"style":1189},[655],[571,2502,1166],{"className":2503},[1193],[571,2505],{"className":2506,"style":1189},[655],[571,2508,2510,2513],{"className":2509},[629],[571,2511],{"className":2512,"style":792},[633],[571,2514,1169],{"className":2515},[638]," hat genau eine reelle Nullstelle: Mindestens eine liefert der Zwischenwertsatz. Hätte ",[571,2518,2520,2533],{"className":2519},[574],[571,2521,2523],{"className":2522},[578],[580,2524,2525],{"xmlns":582},[584,2526,2527,2531],{},[587,2528,2529],{},[590,2530,592],{},[617,2532,592],{"encoding":619},[571,2534,2536],{"className":2535,"ariaHidden":625},[624],[571,2537,2539,2542],{"className":2538},[629],[571,2540],{"className":2541,"style":760},[633],[571,2543,592],{"className":2544,"style":640},[638,639]," zwei, müsste ",[571,2547,2549,2587],{"className":2548},[574],[571,2550,2552],{"className":2551},[578],[580,2553,2554],{"xmlns":582},[584,2555,2556,2584],{},[587,2557,2558,2564,2566,2568,2570,2572,2574,2580,2582],{},[839,2559,2560,2562],{},[590,2561,592],{},[594,2563,847],{"mathvariant":845,"lspace":846,"rspace":846},[594,2565,597],{"stretchy":596},[590,2567,1231],{},[594,2569,603],{"stretchy":596},[594,2571,606],{},[778,2573,1762],{},[839,2575,2576,2578],{},[590,2577,1231],{},[778,2579,1242],{},[594,2581,1252],{},[778,2583,1169],{},[617,2585,2586],{"encoding":619},"f'(x) = 3x^2 + 1",[571,2588,2590,2646,2693],{"className":2589,"ariaHidden":625},[624],[571,2591,2593,2596,2628,2631,2634,2637,2640,2643],{"className":2592},[629],[571,2594],{"className":2595,"style":1579},[633],[571,2597,2599,2602],{"className":2598},[638],[571,2600,592],{"className":2601,"style":640},[638,639],[571,2603,2605],{"className":2604},[874],[571,2606,2608],{"className":2607},[878],[571,2609,2611],{"className":2610},[882],[571,2612,2614],{"className":2613,"style":887},[886],[571,2615,2616,2619],{"style":890},[571,2617],{"className":2618,"style":895},[894],[571,2620,2622],{"className":2621},[899,900,901,902],[571,2623,2625],{"className":2624},[638,902],[571,2626,847],{"className":2627},[638,902],[571,2629,597],{"className":2630},[644],[571,2632,1231],{"className":2633},[638,639],[571,2635,603],{"className":2636},[651],[571,2638],{"className":2639,"style":656},[655],[571,2641,606],{"className":2642},[660],[571,2644],{"className":2645,"style":656},[655],[571,2647,2649,2652,2655,2684,2687,2690],{"className":2648},[629],[571,2650],{"className":2651,"style":1294},[633],[571,2653,1762],{"className":2654},[638],[571,2656,2658,2661],{"className":2657},[638],[571,2659,1231],{"className":2660},[638,639],[571,2662,2664],{"className":2663},[874],[571,2665,2667],{"className":2666},[878],[571,2668,2670],{"className":2669},[882],[571,2671,2673],{"className":2672,"style":1313},[886],[571,2674,2675,2678],{"style":890},[571,2676],{"className":2677,"style":895},[894],[571,2679,2681],{"className":2680},[899,900,901,902],[571,2682,1242],{"className":2683},[638,902],[571,2685],{"className":2686,"style":1189},[655],[571,2688,1252],{"className":2689},[1193],[571,2691],{"className":2692,"style":1189},[655],[571,2694,2696,2699],{"className":2695},[629],[571,2697],{"className":2698,"style":792},[633],[571,2700,1169],{"className":2701},[638]," dazwischen null werden. Das ist unmöglich, denn ",[571,2704,2706,2735],{"className":2705},[574],[571,2707,2709],{"className":2708},[578],[580,2710,2711],{"xmlns":582},[584,2712,2713,2732],{},[587,2714,2715,2717,2723,2725,2727,2730],{},[778,2716,1762],{},[839,2718,2719,2721],{},[590,2720,1231],{},[778,2722,1242],{},[594,2724,1252],{},[778,2726,1169],{},[594,2728,2729],{},"≥",[778,2731,1169],{},[617,2733,2734],{"encoding":619},"3x^2 + 1 \\geq 1",[571,2736,2738,2785,2804],{"className":2737,"ariaHidden":625},[624],[571,2739,2741,2744,2747,2776,2779,2782],{"className":2740},[629],[571,2742],{"className":2743,"style":1294},[633],[571,2745,1762],{"className":2746},[638],[571,2748,2750,2753],{"className":2749},[638],[571,2751,1231],{"className":2752},[638,639],[571,2754,2756],{"className":2755},[874],[571,2757,2759],{"className":2758},[878],[571,2760,2762],{"className":2761},[882],[571,2763,2765],{"className":2764,"style":1313},[886],[571,2766,2767,2770],{"style":890},[571,2768],{"className":2769,"style":895},[894],[571,2771,2773],{"className":2772},[899,900,901,902],[571,2774,1242],{"className":2775},[638,902],[571,2777],{"className":2778,"style":1189},[655],[571,2780,1252],{"className":2781},[1193],[571,2783],{"className":2784,"style":1189},[655],[571,2786,2788,2792,2795,2798,2801],{"className":2787},[629],[571,2789],{"className":2790,"style":2791},[633],"height:0.7804em;vertical-align:-0.136em;",[571,2793,1169],{"className":2794},[638],[571,2796],{"className":2797,"style":656},[655],[571,2799,2729],{"className":2800},[660],[571,2802],{"className":2803,"style":656},[655],[571,2805,2807,2810],{"className":2806},[629],[571,2808],{"className":2809,"style":792},[633],[571,2811,1169],{"className":2812},[638],[558,2814,2816],{"id":2815},"typische-fehler","Typische Fehler",[2818,2819,2820,3165,3253],"ul",{},[2821,2822,2823,2824,1365,2901,2957,2958,3044,3045,3106,3107,3135,3136,3164],"li",{},"Die Differenzierbarkeit übergehen. ",[571,2825,2827,2856],{"className":2826},[574],[571,2828,2830],{"className":2829},[578],[580,2831,2832],{"xmlns":582},[584,2833,2834,2853],{},[587,2835,2836,2838,2840,2842,2844,2846,2849,2851],{},[590,2837,592],{},[594,2839,597],{"stretchy":596},[590,2841,1231],{},[594,2843,603],{"stretchy":596},[594,2845,606],{},[590,2847,2848],{"mathvariant":845},"∣",[590,2850,1231],{},[590,2852,2848],{"mathvariant":845},[617,2854,2855],{"encoding":619},"f(x) = |x|",[571,2857,2859,2886],{"className":2858,"ariaHidden":625},[624],[571,2860,2862,2865,2868,2871,2874,2877,2880,2883],{"className":2861},[629],[571,2863],{"className":2864,"style":634},[633],[571,2866,592],{"className":2867,"style":640},[638,639],[571,2869,597],{"className":2870},[644],[571,2872,1231],{"className":2873},[638,639],[571,2875,603],{"className":2876},[651],[571,2878],{"className":2879,"style":656},[655],[571,2881,606],{"className":2882},[660],[571,2884],{"className":2885,"style":656},[655],[571,2887,2889,2892,2895,2898],{"className":2888},[629],[571,2890],{"className":2891,"style":634},[633],[571,2893,2848],{"className":2894},[638],[571,2896,1231],{"className":2897},[638,639],[571,2899,2848],{"className":2900},[638],[571,2902,2904,2927],{"className":2903},[574],[571,2905,2907],{"className":2906},[578],[580,2908,2909],{"xmlns":582},[584,2910,2911,2925],{},[587,2912,2913,2915,2917,2919,2921,2923],{},[594,2914,1380],{"stretchy":596},[594,2916,1166],{},[778,2918,1169],{},[594,2920,1385],{"separator":625},[778,2922,1169],{},[594,2924,1390],{"stretchy":596},[617,2926,1880],{"encoding":619},[571,2928,2930],{"className":2929,"ariaHidden":625},[624],[571,2931,2933,2936,2939,2942,2945,2948,2951,2954],{"className":2932},[629],[571,2934],{"className":2935,"style":634},[633],[571,2937,1380],{"className":2938},[644],[571,2940,1166],{"className":2941},[638],[571,2943,1169],{"className":2944},[638],[571,2946,1385],{"className":2947},[1412],[571,2949],{"className":2950,"style":1416},[655],[571,2952,1169],{"className":2953},[638],[571,2955,1390],{"className":2956},[651]," hat ",[571,2959,2961,2993],{"className":2960},[574],[571,2962,2964],{"className":2963},[578],[580,2965,2966],{"xmlns":582},[584,2967,2968,2990],{},[587,2969,2970,2972,2974,2976,2978,2980,2982,2984,2986,2988],{},[590,2971,592],{},[594,2973,597],{"stretchy":596},[594,2975,1166],{},[778,2977,1169],{},[594,2979,603],{"stretchy":596},[594,2981,606],{},[590,2983,592],{},[594,2985,597],{"stretchy":596},[778,2987,1169],{},[594,2989,603],{"stretchy":596},[617,2991,2992],{"encoding":619},"f(-1) = f(1)",[571,2994,2996,3026],{"className":2995,"ariaHidden":625},[624],[571,2997,2999,3002,3005,3008,3011,3014,3017,3020,3023],{"className":2998},[629],[571,3000],{"className":3001,"style":634},[633],[571,3003,592],{"className":3004,"style":640},[638,639],[571,3006,597],{"className":3007},[644],[571,3009,1166],{"className":3010},[638],[571,3012,1169],{"className":3013},[638],[571,3015,603],{"className":3016},[651],[571,3018],{"className":3019,"style":656},[655],[571,3021,606],{"className":3022},[660],[571,3024],{"className":3025,"style":656},[655],[571,3027,3029,3032,3035,3038,3041],{"className":3028},[629],[571,3030],{"className":3031,"style":634},[633],[571,3033,592],{"className":3034,"style":640},[638,639],[571,3036,597],{"className":3037},[644],[571,3039,1169],{"className":3040},[638],[571,3042,603],{"className":3043},[651],", aber ",[571,3046,3048,3065],{"className":3047},[574],[571,3049,3051],{"className":3050},[578],[580,3052,3053],{"xmlns":582},[584,3054,3055,3063],{},[587,3056,3057],{},[839,3058,3059,3061],{},[590,3060,592],{},[594,3062,847],{"mathvariant":845,"lspace":846,"rspace":846},[617,3064,984],{"encoding":619},[571,3066,3068],{"className":3067,"ariaHidden":625},[624],[571,3069,3071,3074],{"className":3070},[629],[571,3072],{"className":3073,"style":864},[633],[571,3075,3077,3080],{"className":3076},[638],[571,3078,592],{"className":3079,"style":640},[638,639],[571,3081,3083],{"className":3082},[874],[571,3084,3086],{"className":3085},[878],[571,3087,3089],{"className":3088},[882],[571,3090,3092],{"className":3091,"style":887},[886],[571,3093,3094,3097],{"style":890},[571,3095],{"className":3096,"style":895},[894],[571,3098,3100],{"className":3099},[899,900,901,902],[571,3101,3103],{"className":3102},[638,902],[571,3104,847],{"className":3105},[638,902]," ist nirgends ",[571,3108,3110,3123],{"className":3109},[574],[571,3111,3113],{"className":3112},[578],[580,3114,3115],{"xmlns":582},[584,3116,3117,3121],{},[587,3118,3119],{},[778,3120,780],{},[617,3122,780],{"encoding":619},[571,3124,3126],{"className":3125,"ariaHidden":625},[624],[571,3127,3129,3132],{"className":3128},[629],[571,3130],{"className":3131,"style":792},[633],[571,3133,780],{"className":3134},[638],". Bei ",[571,3137,3139,3152],{"className":3138},[574],[571,3140,3142],{"className":3141},[578],[580,3143,3144],{"xmlns":582},[584,3145,3146,3150],{},[587,3147,3148],{},[778,3149,780],{},[617,3151,780],{"encoding":619},[571,3153,3155],{"className":3154,"ariaHidden":625},[624],[571,3156,3158,3161],{"className":3157},[629],[571,3159],{"className":3160,"style":792},[633],[571,3162,780],{"className":3163},[638]," hat der Graph einen Knick.",[2821,3166,3167,3196,3197,3200,3201,686],{},[571,3168,3170,3184],{"className":3169},[574],[571,3171,3173],{"className":3172},[578],[580,3174,3175],{"xmlns":582},[584,3176,3177,3181],{},[587,3178,3179],{},[590,3180,1550],{},[617,3182,3183],{"encoding":619},"\\xi",[571,3185,3187],{"className":3186,"ariaHidden":625},[624],[571,3188,3190,3193],{"className":3189},[629],[571,3191],{"className":3192,"style":760},[633],[571,3194,1550],{"className":3195,"style":1618},[638,639]," am Rand suchen. Der Satz garantiert eine Stelle ",[567,3198,3199],{},"im Inneren"," ",[571,3202,3204,3226],{"className":3203},[574],[571,3205,3207],{"className":3206},[578],[580,3208,3209],{"xmlns":582},[584,3210,3211,3223],{},[587,3212,3213,3215,3217,3219,3221],{},[594,3214,597],{"stretchy":596},[590,3216,600],{},[594,3218,1385],{"separator":625},[590,3220,613],{},[594,3222,603],{"stretchy":596},[617,3224,3225],{"encoding":619},"(a, b)",[571,3227,3229],{"className":3228,"ariaHidden":625},[624],[571,3230,3232,3235,3238,3241,3244,3247,3250],{"className":3231},[629],[571,3233],{"className":3234,"style":634},[633],[571,3236,597],{"className":3237},[644],[571,3239,600],{"className":3240},[638,639],[571,3242,1385],{"className":3243},[1412],[571,3245],{"className":3246,"style":1416},[655],[571,3248,613],{"className":3249},[638,639],[571,3251,603],{"className":3252},[651],[2821,3254,3255,3256,3378,3379,3456,3457,686],{},"Den Satz auch für ",[571,3257,3259,3290],{"className":3258},[574],[571,3260,3262],{"className":3261},[578],[580,3263,3264],{"xmlns":582},[584,3265,3266,3287],{},[587,3267,3268,3270,3272,3274,3276,3279,3281,3283,3285],{},[590,3269,592],{},[594,3271,597],{"stretchy":596},[590,3273,600],{},[594,3275,603],{"stretchy":596},[594,3277,3278],{"mathvariant":845},"≠",[590,3280,592],{},[594,3282,597],{"stretchy":596},[590,3284,613],{},[594,3286,603],{"stretchy":596},[617,3288,3289],{"encoding":619},"f(a) \\neq f(b)",[571,3291,3293,3360],{"className":3292,"ariaHidden":625},[624],[571,3294,3296,3299,3302,3305,3308,3311,3314,3357],{"className":3295},[629],[571,3297],{"className":3298,"style":634},[633],[571,3300,592],{"className":3301,"style":640},[638,639],[571,3303,597],{"className":3304},[644],[571,3306,600],{"className":3307},[638,639],[571,3309,603],{"className":3310},[651],[571,3312],{"className":3313,"style":656},[655],[571,3315,3317,3350,3354],{"className":3316},[660],[571,3318,3320],{"className":3319},[660],[571,3321,3324],{"className":3322},[638,3323],"vbox",[571,3325,3328],{"className":3326},[3327],"thinbox",[571,3329,3332,3335,3346],{"className":3330},[3331],"rlap",[571,3333],{"className":3334,"style":760},[633],[571,3336,3339],{"className":3337},[3338],"inner",[571,3340,3342],{"className":3341},[638],[571,3343,3345],{"className":3344},[660],"",[571,3347],{"className":3348},[3349],"fix",[571,3351],{"className":3352},[655,3353],"nobreak",[571,3355,606],{"className":3356},[660],[571,3358],{"className":3359,"style":656},[655],[571,3361,3363,3366,3369,3372,3375],{"className":3362},[629],[571,3364],{"className":3365,"style":634},[633],[571,3367,592],{"className":3368,"style":640},[638,639],[571,3370,597],{"className":3371},[644],[571,3373,613],{"className":3374},[638,639],[571,3376,603],{"className":3377},[651]," verwenden. Dann ist der Mittelwertsatz zuständig, und ",[571,3380,3382,3406],{"className":3381},[574],[571,3383,3385],{"className":3384},[578],[580,3386,3387],{"xmlns":582},[584,3388,3389,3403],{},[587,3390,3391,3397,3399,3401],{},[839,3392,3393,3395],{},[590,3394,592],{},[594,3396,847],{"mathvariant":845,"lspace":846,"rspace":846},[594,3398,597],{"stretchy":596},[590,3400,1550],{},[594,3402,603],{"stretchy":596},[617,3404,3405],{"encoding":619},"f'(\\xi)",[571,3407,3409],{"className":3408,"ariaHidden":625},[624],[571,3410,3412,3415,3447,3450,3453],{"className":3411},[629],[571,3413],{"className":3414,"style":1579},[633],[571,3416,3418,3421],{"className":3417},[638],[571,3419,592],{"className":3420,"style":640},[638,639],[571,3422,3424],{"className":3423},[874],[571,3425,3427],{"className":3426},[878],[571,3428,3430],{"className":3429},[882],[571,3431,3433],{"className":3432,"style":887},[886],[571,3434,3435,3438],{"style":890},[571,3436],{"className":3437,"style":895},[894],[571,3439,3441],{"className":3440},[899,900,901,902],[571,3442,3444],{"className":3443},[638,902],[571,3445,847],{"className":3446},[638,902],[571,3448,597],{"className":3449},[644],[571,3451,1550],{"className":3452,"style":1618},[638,639],[571,3454,603],{"className":3455},[651]," ist die Sekantensteigung statt ",[571,3458,3460,3473],{"className":3459},[574],[571,3461,3463],{"className":3462},[578],[580,3464,3465],{"xmlns":582},[584,3466,3467,3471],{},[587,3468,3469],{},[778,3470,780],{},[617,3472,780],{"encoding":619},[571,3474,3476],{"className":3475,"ariaHidden":625},[624],[571,3477,3479,3482],{"className":3478},[629],[571,3480],{"className":3481,"style":792},[633],[571,3483,780],{"className":3484},[638],{"title":3486,"searchDepth":3487,"depth":3487,"links":3488},"",2,[3489,3490,3491],{"id":560,"depth":3487,"text":561},{"id":1209,"depth":3487,"text":1210},{"id":2815,"depth":3487,"text":2816},[3493,3496,3498,3501,3503,3506,3508],{"lhs":3494,"rhs":3495},"0^2 - 4*0 + 1","4^2 - 4*4 + 1",{"lhs":3497,"rhs":780},"2*2 - 4",{"lhs":3499,"rhs":3500},"(-1)^3 - (-1)","1^3 - 1",{"lhs":3502,"rhs":780},"3*(1\u002Fsqrt(3))^2 - 1",{"lhs":3504,"rhs":3505},"round(1\u002Fsqrt(3), 3)","0.577",{"lhs":3507,"rhs":780},"round(((x + 1e-5)^3 + (x + 1e-5) - ((x - 1e-5)^3 + (x - 1e-5)))\u002F2e-5 - (3*x^2 + 1), 6)",{"lhs":3509,"rhs":3510},"abs(-1)","abs(1)","a \u003C b,\\ f \\text{ stetig auf } [a, b],\\ f \\text{ differenzierbar auf } (a, b)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo><\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a < b,\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:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\"><\u003C\u002Fspan>\u003Cspan 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