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Vorzeichen.",[564,1120,1121,1299,1300,1399,1400,1505,1506,1534,1535,1563,1564,1704],{},[583,1122,1124,1161],{"className":1123},[586],[583,1125,1127],{"className":1126},[590],[592,1128,1129],{"xmlns":594},[596,1130,1131,1159],{},[599,1132,1133,1145,1147,1153,1155,1157],{},[602,1134,1135,1137],{},[605,1136,607],{},[599,1138,1139,1141,1143],{},[611,1140,614],{"mathvariant":613},[611,1142,614],{"mathvariant":613},[611,1144,614],{"mathvariant":613},[611,1146,620],{"stretchy":619},[622,1148,1149,1151],{},[605,1150,626],{},[628,1152,630],{},[611,1154,633],{"stretchy":619},[611,1156,825],{"mathvariant":613},[628,1158,630],{},[640,1160,830],{"encoding":642},[583,1162,1164,1290],{"className":1163,"ariaHidden":648},[647],[583,1165,1167,1170,1202,1205,1245,1248,1251,1287],{"className":1166},[652],[583,1168],{"className":1169,"style":657},[656],[583,1171,1173,1176],{"className":1172},[661],[583,1174,607],{"className":1175,"style":666},[661,665],[583,1177,1179],{"className":1178},[670],[583,1180,1182],{"className":1181},[674],[583,1183,1185],{"className":1184},[678],[583,1186,1188],{"className":1187,"style":683},[682],[583,1189,1190,1193],{"style":686},[583,1191],{"className":1192,"style":691},[690],[583,1194,1196],{"className":1195},[695,696,697,698],[583,1197,1199],{"className":1198},[661,698],[583,1200,872],{"className":1201},[661,698],[583,1203,620],{"className":1204},[709],[583,1206,1208,1211],{"className":1207},[661],[583,1209,626],{"className":1210},[661,665],[583,1212,1214],{"className":1213},[670],[583,1215,1217,1237],{"className":1216},[674,722],[583,1218,1220,1234],{"className":1219},[678],[583,1221,1223],{"className":1222,"style":729},[682],[583,1224,1225,1228],{"style":732},[583,1226],{"className":1227,"style":691},[690],[583,1229,1231],{"className":1230},[695,696,697,698],[583,1232,630],{"className":1233},[661,698],[583,1235,746],{"className":1236},[745],[583,1238,1240],{"className":1239},[678],[583,1241,1243],{"className":1242,"style":753},[682],[583,1244],{},[583,1246,633],{"className":1247},[759],[583,1249],{"className":1250,"style":764},[763],[583,1252,1254,1281,1284],{"className":1253},[768],[583,1255,1257],{"className":1256},[768],[583,1258,1260],{"className":1259},[661,931],[583,1261,1263],{"className":1262},[935],[583,1264,1266,1269,1278],{"className":1265},[939],[583,1267],{"className":1268,"style":943},[656],[583,1270,1272],{"className":1271},[947],[583,1273,1275],{"className":1274},[661],[583,1276,954],{"className":1277},[768],[583,1279],{"className":1280},[958],[583,1282],{"className":1283},[763,962],[583,1285,636],{"className":1286},[768],[583,1288],{"className":1289,"style":764},[763],[583,1291,1293,1296],{"className":1292},[652],[583,1294],{"className":1295,"style":778},[656],[583,1297,630],{"className":1298},[661]," ist hinreichend, aber nicht notwendig: Bei ",[583,1301,1303,1332],{"className":1302},[586],[583,1304,1306],{"className":1305},[590],[592,1307,1308],{"xmlns":594},[596,1309,1310,1329],{},[599,1311,1312,1314,1316,1318,1320,1322],{},[605,1313,607],{},[611,1315,620],{"stretchy":619},[605,1317,626],{},[611,1319,633],{"stretchy":619},[611,1321,636],{},[602,1323,1324,1326],{},[605,1325,626],{},[628,1327,1328],{},"5",[640,1330,1331],{"encoding":642},"f(x) = x^5",[583,1333,1335,1363],{"className":1334,"ariaHidden":648},[647],[583,1336,1338,1342,1345,1348,1351,1354,1357,1360],{"className":1337},[652],[583,1339],{"className":1340,"style":1341},[656],"height:1em;vertical-align:-0.25em;",[583,1343,607],{"className":1344,"style":666},[661,665],[583,1346,620],{"className":1347},[709],[583,1349,626],{"className":1350},[661,665],[583,1352,633],{"className":1353},[759],[583,1355],{"className":1356,"style":764},[763],[583,1358,636],{"className":1359},[768],[583,1361],{"className":1362,"style":764},[763],[583,1364,1366,1370],{"className":1365},[652],[583,1367],{"className":1368,"style":1369},[656],"height:0.8141em;",[583,1371,1373,1376],{"className":1372},[661],[583,1374,626],{"className":1375},[661,665],[583,1377,1379],{"className":1378},[670],[583,1380,1382],{"className":1381},[674],[583,1383,1385],{"className":1384},[678],[583,1386,1388],{"className":1387,"style":1369},[682],[583,1389,1390,1393],{"style":686},[583,1391],{"className":1392,"style":691},[690],[583,1394,1396],{"className":1395},[695,696,697,698],[583,1397,1328],{"className":1398},[661,698]," ist ",[583,1401,1403,1437],{"className":1402},[586],[583,1404,1406],{"className":1405},[590],[592,1407,1408],{"xmlns":594},[596,1409,1410,1434],{},[599,1411,1412,1424,1426,1428,1430,1432],{},[602,1413,1414,1416],{},[605,1415,607],{},[599,1417,1418,1420,1422],{},[611,1419,614],{"mathvariant":613},[611,1421,614],{"mathvariant":613},[611,1423,614],{"mathvariant":613},[611,1425,620],{"stretchy":619},[628,1427,630],{},[611,1429,633],{"stretchy":619},[611,1431,636],{},[628,1433,630],{},[640,1435,1436],{"encoding":642},"f'''(0) = 0",[583,1438,1440,1496],{"className":1439,"ariaHidden":648},[647],[583,1441,1443,1446,1478,1481,1484,1487,1490,1493],{"className":1442},[652],[583,1444],{"className":1445,"style":657},[656],[583,1447,1449,1452],{"className":1448},[661],[583,1450,607],{"className":1451,"style":666},[661,665],[583,1453,1455],{"className":1454},[670],[583,1456,1458],{"className":1457},[674],[583,1459,1461],{"className":1460},[678],[583,1462,1464],{"className":1463,"style":683},[682],[583,1465,1466,1469],{"style":686},[583,1467],{"className":1468,"style":691},[690],[583,1470,1472],{"className":1471},[695,696,697,698],[583,1473,1475],{"className":1474},[661,698],[583,1476,872],{"className":1477},[661,698],[583,1479,620],{"className":1480},[709],[583,1482,630],{"className":1483},[661],[583,1485,633],{"className":1486},[759],[583,1488],{"className":1489,"style":764},[763],[583,1491,636],{"className":1492},[768],[583,1494],{"className":1495,"style":764},[763],[583,1497,1499,1502],{"className":1498},[652],[583,1500],{"className":1501,"style":778},[656],[583,1503,630],{"className":1504},[661],", und trotzdem hat ",[583,1507,1509,1522],{"className":1508},[586],[583,1510,1512],{"className":1511},[590],[592,1513,1514],{"xmlns":594},[596,1515,1516,1520],{},[599,1517,1518],{},[605,1519,607],{},[640,1521,607],{"encoding":642},[583,1523,1525],{"className":1524,"ariaHidden":648},[647],[583,1526,1528,1531],{"className":1527},[652],[583,1529],{"className":1530,"style":943},[656],[583,1532,607],{"className":1533,"style":666},[661,665]," bei ",[583,1536,1538,1551],{"className":1537},[586],[583,1539,1541],{"className":1540},[590],[592,1542,1543],{"xmlns":594},[596,1544,1545,1549],{},[599,1546,1547],{},[628,1548,630],{},[640,1550,630],{"encoding":642},[583,1552,1554],{"className":1553,"ariaHidden":648},[647],[583,1555,1557,1560],{"className":1556},[652],[583,1558],{"className":1559,"style":778},[656],[583,1561,630],{"className":1562},[661]," eine Wendestelle, weil ",[583,1565,1567,1607],{"className":1566},[586],[583,1568,1570],{"className":1569},[590],[592,1571,1572],{"xmlns":594},[596,1573,1574,1604],{},[599,1575,1576,1586,1588,1590,1592,1594,1597],{},[602,1577,1578,1580],{},[605,1579,607],{},[599,1581,1582,1584],{},[611,1583,614],{"mathvariant":613},[611,1585,614],{"mathvariant":613},[611,1587,620],{"stretchy":619},[605,1589,626],{},[611,1591,633],{"stretchy":619},[611,1593,636],{},[628,1595,1596],{},"20",[602,1598,1599,1601],{},[605,1600,626],{},[628,1602,1603],{},"3",[640,1605,1606],{"encoding":642},"f''(x) = 20x^3",[583,1608,1610,1666],{"className":1609,"ariaHidden":648},[647],[583,1611,1613,1616,1648,1651,1654,1657,1660,1663],{"className":1612},[652],[583,1614],{"className":1615,"style":657},[656],[583,1617,1619,1622],{"className":1618},[661],[583,1620,607],{"className":1621,"style":666},[661,665],[583,1623,1625],{"className":1624},[670],[583,1626,1628],{"className":1627},[674],[583,1629,1631],{"className":1630},[678],[583,1632,1634],{"className":1633,"style":683},[682],[583,1635,1636,1639],{"style":686},[583,1637],{"className":1638,"style":691},[690],[583,1640,1642],{"className":1641},[695,696,697,698],[583,1643,1645],{"className":1644},[661,698],[583,1646,705],{"className":1647},[661,698],[583,1649,620],{"className":1650},[709],[583,1652,626],{"className":1653},[661,665],[583,1655,633],{"className":1656},[759],[583,1658],{"className":1659,"style":764},[763],[583,1661,636],{"className":1662},[768],[583,1664],{"className":1665,"style":764},[763],[583,1667,1669,1672,1675],{"className":1668},[652],[583,1670],{"className":1671,"style":1369},[656],[583,1673,1596],{"className":1674},[661],[583,1676,1678,1681],{"className":1677},[661],[583,1679,626],{"className":1680},[661,665],[583,1682,1684],{"className":1683},[670],[583,1685,1687],{"className":1686},[674],[583,1688,1690],{"className":1689},[678],[583,1691,1693],{"className":1692,"style":1369},[682],[583,1694,1695,1698],{"style":686},[583,1696],{"className":1697,"style":691},[690],[583,1699,1701],{"className":1700},[695,696,697,698],[583,1702,1603],{"className":1703},[661,698]," dort das Vorzeichen wechselt.",[564,1706,1707,1708,1849,1850,1853],{},"Ist zusätzlich ",[583,1709,1711,1744],{"className":1710},[586],[583,1712,1714],{"className":1713},[590],[592,1715,1716],{"xmlns":594},[596,1717,1718,1741],{},[599,1719,1720,1727,1729,1735,1737,1739],{},[602,1721,1722,1724],{},[605,1723,607],{},[611,1725,614],{"mathvariant":613,"lspace":1726,"rspace":1726},"0em",[611,1728,620],{"stretchy":619},[622,1730,1731,1733],{},[605,1732,626],{},[628,1734,630],{},[611,1736,633],{"stretchy":619},[611,1738,636],{},[628,1740,630],{},[640,1742,1743],{"encoding":642},"f'(x_0) = 0",[583,1745,1747,1840],{"className":1746,"ariaHidden":648},[647],[583,1748,1750,1753,1785,1788,1828,1831,1834,1837],{"className":1749},[652],[583,1751],{"className":1752,"style":657},[656],[583,1754,1756,1759],{"className":1755},[661],[583,1757,607],{"className":1758,"style":666},[661,665],[583,1760,1762],{"className":1761},[670],[583,1763,1765],{"className":1764},[674],[583,1766,1768],{"className":1767},[678],[583,1769,1771],{"className":1770,"style":683},[682],[583,1772,1773,1776],{"style":686},[583,1774],{"className":1775,"style":691},[690],[583,1777,1779],{"className":1778},[695,696,697,698],[583,1780,1782],{"className":1781},[661,698],[583,1783,614],{"className":1784},[661,698],[583,1786,620],{"className":1787},[709],[583,1789,1791,1794],{"className":1790},[661],[583,1792,626],{"className":1793},[661,665],[583,1795,1797],{"className":1796},[670],[583,1798,1800,1820],{"className":1799},[674,722],[583,1801,1803,1817],{"className":1802},[678],[583,1804,1806],{"className":1805,"style":729},[682],[583,1807,1808,1811],{"style":732},[583,1809],{"className":1810,"style":691},[690],[583,1812,1814],{"className":1813},[695,696,697,698],[583,1815,630],{"className":1816},[661,698],[583,1818,746],{"className":1819},[745],[583,1821,1823],{"className":1822},[678],[583,1824,1826],{"className":1825,"style":753},[682],[583,1827],{},[583,1829,633],{"className":1830},[759],[583,1832],{"className":1833,"style":764},[763],[583,1835,636],{"className":1836},[768],[583,1838],{"className":1839,"style":764},[763],[583,1841,1843,1846],{"className":1842},[652],[583,1844],{"className":1845,"style":778},[656],[583,1847,630],{"className":1848},[661],", hat der Wendepunkt eine waagerechte Tangente. Er heißt dann ",[568,1851,1852],{},"Sattelpunkt"," oder Terrassenpunkt.",[564,1855,1856,1857,782],{},"Die Tangente im Wendepunkt heißt ",[568,1858,1859],{},"Wendetangente",[559,1861,1863],{"id":1862},"beispiele","Beispiele",[564,1865,1866,2047,2048,2210,2211,2342,2343,782],{},[583,1867,1869,1914],{"className":1868},[586],[583,1870,1872],{"className":1871},[590],[592,1873,1874],{"xmlns":594},[596,1875,1876,1911],{},[599,1877,1878,1880,1882,1884,1886,1888,1894,1897,1899,1906,1909],{},[605,1879,607],{},[611,1881,620],{"stretchy":619},[605,1883,626],{},[611,1885,633],{"stretchy":619},[611,1887,636],{},[602,1889,1890,1892],{},[605,1891,626],{},[628,1893,1603],{},[611,1895,1896],{},"−",[628,1898,1603],{},[602,1900,1901,1903],{},[605,1902,626],{},[628,1904,1905],{},"2",[611,1907,1908],{},"+",[628,1910,1905],{},[640,1912,1913],{"encoding":642},"f(x) = x^3 - 3x^2 + 2",[583,1915,1917,1944,1991,2038],{"className":1916,"ariaHidden":648},[647],[583,1918,1920,1923,1926,1929,1932,1935,1938,1941],{"className":1919},[652],[583,1921],{"className":1922,"style":1341},[656],[583,1924,607],{"className":1925,"style":666},[661,665],[583,1927,620],{"className":1928},[709],[583,1930,626],{"className":1931},[661,665],[583,1933,633],{"className":1934},[759],[583,1936],{"className":1937,"style":764},[763],[583,1939,636],{"className":1940},[768],[583,1942],{"className":1943,"style":764},[763],[583,1945,1947,1951,1980,1984,1988],{"className":1946},[652],[583,1948],{"className":1949,"style":1950},[656],"height:0.8974em;vertical-align:-0.0833em;",[583,1952,1954,1957],{"className":1953},[661],[583,1955,626],{"className":1956},[661,665],[583,1958,1960],{"className":1959},[670],[583,1961,1963],{"className":1962},[674],[583,1964,1966],{"className":1965},[678],[583,1967,1969],{"className":1968,"style":1369},[682],[583,1970,1971,1974],{"style":686},[583,1972],{"className":1973,"style":691},[690],[583,1975,1977],{"className":1976},[695,696,697,698],[583,1978,1603],{"className":1979},[661,698],[583,1981],{"className":1982,"style":1983},[763],"margin-right:0.2222em;",[583,1985,1896],{"className":1986},[1987],"mbin",[583,1989],{"className":1990,"style":1983},[763],[583,1992,1994,1997,2000,2029,2032,2035],{"className":1993},[652],[583,1995],{"className":1996,"style":1950},[656],[583,1998,1603],{"className":1999},[661],[583,2001,2003,2006],{"className":2002},[661],[583,2004,626],{"className":2005},[661,665],[583,2007,2009],{"className":2008},[670],[583,2010,2012],{"className":2011},[674],[583,2013,2015],{"className":2014},[678],[583,2016,2018],{"className":2017,"style":1369},[682],[583,2019,2020,2023],{"style":686},[583,2021],{"className":2022,"style":691},[690],[583,2024,2026],{"className":2025},[695,696,697,698],[583,2027,1905],{"className":2028},[661,698],[583,2030],{"className":2031,"style":1983},[763],[583,2033,1908],{"className":2034},[1987],[583,2036],{"className":2037,"style":1983},[763],[583,2039,2041,2044],{"className":2040},[652],[583,2042],{"className":2043,"style":778},[656],[583,2045,1905],{"className":2046},[661]," mit ",[583,2049,2051,2092],{"className":2050},[586],[583,2052,2054],{"className":2053},[590],[592,2055,2056],{"xmlns":594},[596,2057,2058,2089],{},[599,2059,2060,2066,2068,2070,2072,2074,2076,2082,2084,2087],{},[602,2061,2062,2064],{},[605,2063,607],{},[611,2065,614],{"mathvariant":613,"lspace":1726,"rspace":1726},[611,2067,620],{"stretchy":619},[605,2069,626],{},[611,2071,633],{"stretchy":619},[611,2073,636],{},[628,2075,1603],{},[602,2077,2078,2080],{},[605,2079,626],{},[628,2081,1905],{},[611,2083,1896],{},[628,2085,2086],{},"6",[605,2088,626],{},[640,2090,2091],{"encoding":642},"f'(x) = 3x^2 - 6x",[583,2093,2095,2151,2198],{"className":2094,"ariaHidden":648},[647],[583,2096,2098,2101,2133,2136,2139,2142,2145,2148],{"className":2097},[652],[583,2099],{"className":2100,"style":657},[656],[583,2102,2104,2107],{"className":2103},[661],[583,2105,607],{"className":2106,"style":666},[661,665],[583,2108,2110],{"className":2109},[670],[583,2111,2113],{"className":2112},[674],[583,2114,2116],{"className":2115},[678],[583,2117,2119],{"className":2118,"style":683},[682],[583,2120,2121,2124],{"style":686},[583,2122],{"className":2123,"style":691},[690],[583,2125,2127],{"className":2126},[695,696,697,698],[583,2128,2130],{"className":2129},[661,698],[583,2131,614],{"className":2132},[661,698],[583,2134,620],{"className":2135},[709],[583,2137,626],{"className":2138},[661,665],[583,2140,633],{"className":2141},[759],[583,2143],{"className":2144,"style":764},[763],[583,2146,636],{"className":2147},[768],[583,2149],{"className":2150,"style":764},[763],[583,2152,2154,2157,2160,2189,2192,2195],{"className":2153},[652],[583,2155],{"className":2156,"style":1950},[656],[583,2158,1603],{"className":2159},[661],[583,2161,2163,2166],{"className":2162},[661],[583,2164,626],{"className":2165},[661,665],[583,2167,2169],{"className":2168},[670],[583,2170,2172],{"className":2171},[674],[583,2173,2175],{"className":2174},[678],[583,2176,2178],{"className":2177,"style":1369},[682],[583,2179,2180,2183],{"style":686},[583,2181],{"className":2182,"style":691},[690],[583,2184,2186],{"className":2185},[695,696,697,698],[583,2187,1905],{"className":2188},[661,698],[583,2190],{"className":2191,"style":1983},[763],[583,2193,1896],{"className":2194},[1987],[583,2196],{"className":2197,"style":1983},[763],[583,2199,2201,2204,2207],{"className":2200},[652],[583,2202],{"className":2203,"style":778},[656],[583,2205,2086],{"className":2206},[661],[583,2208,626],{"className":2209},[661,665],", ",[583,2212,2214,2252],{"className":2213},[586],[583,2215,2217],{"className":2216},[590],[592,2218,2219],{"xmlns":594},[596,2220,2221,2249],{},[599,2222,2223,2233,2235,2237,2239,2241,2243,2245,2247],{},[602,2224,2225,2227],{},[605,2226,607],{},[599,2228,2229,2231],{},[611,2230,614],{"mathvariant":613},[611,2232,614],{"mathvariant":613},[611,2234,620],{"stretchy":619},[605,2236,626],{},[611,2238,633],{"stretchy":619},[611,2240,636],{},[628,2242,2086],{},[605,2244,626],{},[611,2246,1896],{},[628,2248,2086],{},[640,2250,2251],{"encoding":642},"f''(x) = 6x - 6",[583,2253,2255,2311,2333],{"className":2254,"ariaHidden":648},[647],[583,2256,2258,2261,2293,2296,2299,2302,2305,2308],{"className":2257},[652],[583,2259],{"className":2260,"style":657},[656],[583,2262,2264,2267],{"className":2263},[661],[583,2265,607],{"className":2266,"style":666},[661,665],[583,2268,2270],{"className":2269},[670],[583,2271,2273],{"className":2272},[674],[583,2274,2276],{"className":2275},[678],[583,2277,2279],{"className":2278,"style":683},[682],[583,2280,2281,2284],{"style":686},[583,2282],{"className":2283,"style":691},[690],[583,2285,2287],{"className":2286},[695,696,697,698],[583,2288,2290],{"className":2289},[661,698],[583,2291,705],{"className":2292},[661,698],[583,2294,620],{"className":2295},[709],[583,2297,626],{"className":2298},[661,665],[583,2300,633],{"className":2301},[759],[583,2303],{"className":2304,"style":764},[763],[583,2306,636],{"className":2307},[768],[583,2309],{"className":2310,"style":764},[763],[583,2312,2314,2318,2321,2324,2327,2330],{"className":2313},[652],[583,2315],{"className":2316,"style":2317},[656],"height:0.7278em;vertical-align:-0.0833em;",[583,2319,2086],{"className":2320},[661],[583,2322,626],{"className":2323},[661,665],[583,2325],{"className":2326,"style":1983},[763],[583,2328,1896],{"className":2329},[1987],[583,2331],{"className":2332,"style":1983},[763],[583,2334,2336,2339],{"className":2335},[652],[583,2337],{"className":2338,"style":778},[656],[583,2340,2086],{"className":2341},[661]," und ",[583,2344,2346,2380],{"className":2345},[586],[583,2347,2349],{"className":2348},[590],[592,2350,2351],{"xmlns":594},[596,2352,2353,2377],{},[599,2354,2355,2367,2369,2371,2373,2375],{},[602,2356,2357,2359],{},[605,2358,607],{},[599,2360,2361,2363,2365],{},[611,2362,614],{"mathvariant":613},[611,2364,614],{"mathvariant":613},[611,2366,614],{"mathvariant":613},[611,2368,620],{"stretchy":619},[605,2370,626],{},[611,2372,633],{"stretchy":619},[611,2374,636],{},[628,2376,2086],{},[640,2378,2379],{"encoding":642},"f'''(x) = 6",[583,2381,2383,2439],{"className":2382,"ariaHidden":648},[647],[583,2384,2386,2389,2421,2424,2427,2430,2433,2436],{"className":2385},[652],[583,2387],{"className":2388,"style":657},[656],[583,2390,2392,2395],{"className":2391},[661],[583,2393,607],{"className":2394,"style":666},[661,665],[583,2396,2398],{"className":2397},[670],[583,2399,2401],{"className":2400},[674],[583,2402,2404],{"className":2403},[678],[583,2405,2407],{"className":2406,"style":683},[682],[583,2408,2409,2412],{"style":686},[583,2410],{"className":2411,"style":691},[690],[583,2413,2415],{"className":2414},[695,696,697,698],[583,2416,2418],{"className":2417},[661,698],[583,2419,872],{"className":2420},[661,698],[583,2422,620],{"className":2423},[709],[583,2425,626],{"className":2426},[661,665],[583,2428,633],{"className":2429},[759],[583,2431],{"className":2432,"style":764},[763],[583,2434,636],{"className":2435},[768],[583,2437],{"className":2438,"style":764},[763],[583,2440,2442,2445],{"className":2441},[652],[583,2443],{"className":2444,"style":778},[656],[583,2446,2086],{"className":2447},[661],[564,2449,2450,2553,2554,2607,2608,2768,2769,1399,2835,2904,2905,3009],{},[583,2451,2453,2485],{"className":2452},[586],[583,2454,2456],{"className":2455},[590],[592,2457,2458],{"xmlns":594},[596,2459,2460,2482],{},[599,2461,2462,2472,2474,2476,2478,2480],{},[602,2463,2464,2466],{},[605,2465,607],{},[599,2467,2468,2470],{},[611,2469,614],{"mathvariant":613},[611,2471,614],{"mathvariant":613},[611,2473,620],{"stretchy":619},[605,2475,626],{},[611,2477,633],{"stretchy":619},[611,2479,636],{},[628,2481,630],{},[640,2483,2484],{"encoding":642},"f''(x) = 0",[583,2486,2488,2544],{"className":2487,"ariaHidden":648},[647],[583,2489,2491,2494,2526,2529,2532,2535,2538,2541],{"className":2490},[652],[583,2492],{"className":2493,"style":657},[656],[583,2495,2497,2500],{"className":2496},[661],[583,2498,607],{"className":2499,"style":666},[661,665],[583,2501,2503],{"className":2502},[670],[583,2504,2506],{"className":2505},[674],[583,2507,2509],{"className":2508},[678],[583,2510,2512],{"className":2511,"style":683},[682],[583,2513,2514,2517],{"style":686},[583,2515],{"className":2516,"style":691},[690],[583,2518,2520],{"className":2519},[695,696,697,698],[583,2521,2523],{"className":2522},[661,698],[583,2524,705],{"className":2525},[661,698],[583,2527,620],{"className":2528},[709],[583,2530,626],{"className":2531},[661,665],[583,2533,633],{"className":2534},[759],[583,2536],{"className":2537,"style":764},[763],[583,2539,636],{"className":2540},[768],[583,2542],{"className":2543,"style":764},[763],[583,2545,2547,2550],{"className":2546},[652],[583,2548],{"className":2549,"style":778},[656],[583,2551,630],{"className":2552},[661]," ergibt ",[583,2555,2557,2576],{"className":2556},[586],[583,2558,2560],{"className":2559},[590],[592,2561,2562],{"xmlns":594},[596,2563,2564,2573],{},[599,2565,2566,2568,2570],{},[605,2567,626],{},[611,2569,636],{},[628,2571,2572],{},"1",[640,2574,2575],{"encoding":642},"x = 1",[583,2577,2579,2598],{"className":2578,"ariaHidden":648},[647],[583,2580,2582,2586,2589,2592,2595],{"className":2581},[652],[583,2583],{"className":2584,"style":2585},[656],"height:0.4306em;",[583,2587,626],{"className":2588},[661,665],[583,2590],{"className":2591,"style":764},[763],[583,2593,636],{"className":2594},[768],[583,2596],{"className":2597,"style":764},[763],[583,2599,2601,2604],{"className":2600},[652],[583,2602],{"className":2603,"style":778},[656],[583,2605,2572],{"className":2606},[661],", und ",[583,2609,2611,2649],{"className":2610},[586],[583,2612,2614],{"className":2613},[590],[592,2615,2616],{"xmlns":594},[596,2617,2618,2646],{},[599,2619,2620,2632,2634,2636,2638,2640,2642,2644],{},[602,2621,2622,2624],{},[605,2623,607],{},[599,2625,2626,2628,2630],{},[611,2627,614],{"mathvariant":613},[611,2629,614],{"mathvariant":613},[611,2631,614],{"mathvariant":613},[611,2633,620],{"stretchy":619},[628,2635,2572],{},[611,2637,633],{"stretchy":619},[611,2639,636],{},[628,2641,2086],{},[611,2643,825],{"mathvariant":613},[628,2645,630],{},[640,2647,2648],{"encoding":642},"f'''(1) = 6 \\neq 0",[583,2650,2652,2708,2759],{"className":2651,"ariaHidden":648},[647],[583,2653,2655,2658,2690,2693,2696,2699,2702,2705],{"className":2654},[652],[583,2656],{"className":2657,"style":657},[656],[583,2659,2661,2664],{"className":2660},[661],[583,2662,607],{"className":2663,"style":666},[661,665],[583,2665,2667],{"className":2666},[670],[583,2668,2670],{"className":2669},[674],[583,2671,2673],{"className":2672},[678],[583,2674,2676],{"className":2675,"style":683},[682],[583,2677,2678,2681],{"style":686},[583,2679],{"className":2680,"style":691},[690],[583,2682,2684],{"className":2683},[695,696,697,698],[583,2685,2687],{"className":2686},[661,698],[583,2688,872],{"className":2689},[661,698],[583,2691,620],{"className":2692},[709],[583,2694,2572],{"className":2695},[661],[583,2697,633],{"className":2698},[759],[583,2700],{"className":2701,"style":764},[763],[583,2703,636],{"className":2704},[768],[583,2706],{"className":2707,"style":764},[763],[583,2709,2711,2714,2717,2720,2756],{"className":2710},[652],[583,2712],{"className":2713,"style":943},[656],[583,2715,2086],{"className":2716},[661],[583,2718],{"className":2719,"style":764},[763],[583,2721,2723,2750,2753],{"className":2722},[768],[583,2724,2726],{"className":2725},[768],[583,2727,2729],{"className":2728},[661,931],[583,2730,2732],{"className":2731},[935],[583,2733,2735,2738,2747],{"className":2734},[939],[583,2736],{"className":2737,"style":943},[656],[583,2739,2741],{"className":2740},[947],[583,2742,2744],{"className":2743},[661],[583,2745,954],{"className":2746},[768],[583,2748],{"className":2749},[958],[583,2751],{"className":2752},[763,962],[583,2754,636],{"className":2755},[768],[583,2757],{"className":2758,"style":764},[763],[583,2760,2762,2765],{"className":2761},[652],[583,2763],{"className":2764,"style":778},[656],[583,2766,630],{"className":2767},[661],". Mit ",[583,2770,2772,2796],{"className":2771},[586],[583,2773,2775],{"className":2774},[590],[592,2776,2777],{"xmlns":594},[596,2778,2779,2793],{},[599,2780,2781,2783,2785,2787,2789,2791],{},[605,2782,607],{},[611,2784,620],{"stretchy":619},[628,2786,2572],{},[611,2788,633],{"stretchy":619},[611,2790,636],{},[628,2792,630],{},[640,2794,2795],{"encoding":642},"f(1) = 0",[583,2797,2799,2826],{"className":2798,"ariaHidden":648},[647],[583,2800,2802,2805,2808,2811,2814,2817,2820,2823],{"className":2801},[652],[583,2803],{"className":2804,"style":1341},[656],[583,2806,607],{"className":2807,"style":666},[661,665],[583,2809,620],{"className":2810},[709],[583,2812,2572],{"className":2813},[661],[583,2815,633],{"className":2816},[759],[583,2818],{"className":2819,"style":764},[763],[583,2821,636],{"className":2822},[768],[583,2824],{"className":2825,"style":764},[763],[583,2827,2829,2832],{"className":2828},[652],[583,2830],{"className":2831,"style":778},[656],[583,2833,630],{"className":2834},[661],[583,2836,2838,2864],{"className":2837},[586],[583,2839,2841],{"className":2840},[590],[592,2842,2843],{"xmlns":594},[596,2844,2845,2861],{},[599,2846,2847,2850,2852,2854,2857,2859],{},[605,2848,2849],{},"W",[611,2851,620],{"stretchy":619},[628,2853,2572],{},[611,2855,2856],{},"∣",[628,2858,630],{},[611,2860,633],{"stretchy":619},[640,2862,2863],{"encoding":642},"W(1 \\mid 0)",[583,2865,2867,2892],{"className":2866,"ariaHidden":648},[647],[583,2868,2870,2873,2877,2880,2883,2886,2889],{"className":2869},[652],[583,2871],{"className":2872,"style":1341},[656],[583,2874,2849],{"className":2875,"style":2876},[661,665],"margin-right:0.1389em;",[583,2878,620],{"className":2879},[709],[583,2881,2572],{"className":2882},[661],[583,2884],{"className":2885,"style":764},[763],[583,2887,2856],{"className":2888},[768],[583,2890],{"className":2891,"style":764},[763],[583,2893,2895,2898,2901],{"className":2894},[652],[583,2896],{"className":2897,"style":1341},[656],[583,2899,630],{"className":2900},[661],[583,2902,633],{"className":2903},[759]," ein Wendepunkt. Wegen ",[583,2906,2908,2938],{"className":2907},[586],[583,2909,2911],{"className":2910},[590],[592,2912,2913],{"xmlns":594},[596,2914,2915,2935],{},[599,2916,2917,2923,2925,2927,2929,2931,2933],{},[602,2918,2919,2921],{},[605,2920,607],{},[611,2922,614],{"mathvariant":613,"lspace":1726,"rspace":1726},[611,2924,620],{"stretchy":619},[628,2926,2572],{},[611,2928,633],{"stretchy":619},[611,2930,636],{},[611,2932,1896],{},[628,2934,1603],{},[640,2936,2937],{"encoding":642},"f'(1) = 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lautet die Wendetangente",[583,3011,3014],{"className":3012},[3013],"katex-display",[583,3015,3017,3074],{"className":3016},[586],[583,3018,3020],{"className":3019},[590],[592,3021,3023],{"xmlns":594,"display":3022},"block",[596,3024,3025,3071],{},[599,3026,3027,3030,3032,3034,3036,3038,3040,3042,3045,3047,3049,3051,3053,3055,3057,3059,3061,3063,3065,3067,3069],{},[605,3028,3029],{},"t",[611,3031,620],{"stretchy":619},[605,3033,626],{},[611,3035,633],{"stretchy":619},[611,3037,636],{},[611,3039,1896],{},[628,3041,1603],{},[611,3043,3044],{},"⋅",[611,3046,620],{"stretchy":619},[605,3048,626],{},[611,3050,1896],{},[628,3052,2572],{},[611,3054,633],{"stretchy":619},[611,3056,1908],{},[628,3058,630],{},[611,3060,636],{},[611,3062,1896],{},[628,3064,1603],{},[605,3066,626],{},[611,3068,1908],{},[628,3070,1603],{},[640,3072,3073],{"encoding":642},"t(x) = -3 \\cdot (x - 1) + 0 = -3x + 3",[583,3075,3077,3104,3125,3146,3167,3185,3209],{"className":3076,"ariaHidden":648},[647],[583,3078,3080,3083,3086,3089,3092,3095,3098,3101],{"className":3079},[652],[583,3081],{"className":3082,"style":1341},[656],[583,3084,3029],{"className":3085},[661,665],[583,3087,620],{"className":3088},[709],[583,3090,626],{"className":3091},[661,665],[583,3093,633],{"className":3094},[759],[583,3096],{"className":3097,"style":764},[763],[583,3099,636],{"className":3100},[768],[583,3102],{"className":3103,"style":764},[763],[583,3105,3107,3110,3113,3116,3119,3122],{"className":3106},[652],[583,3108],{"className":3109,"style":2317},[656],[583,3111,1896],{"className":3112},[661],[583,3114,1603],{"className":3115},[661],[583,3117],{"className":3118,"style":1983},[763],[583,3120,3044],{"className":3121},[1987],[583,3123],{"className":3124,"style":1983},[763],[583,3126,3128,3131,3134,3137,3140,3143],{"className":3127},[652],[583,3129],{"className":3130,"style":1341},[656],[583,3132,620],{"className":3133},[709],[583,3135,626],{"className":3136},[661,665],[583,3138],{"className":3139,"style":1983},[763],[583,3141,1896],{"className":3142},[1987],[583,3144],{"className":3145,"style":1983},[763],[583,3147,3149,3152,3155,3158,3161,3164],{"className":3148},[652],[583,3150],{"className":3151,"style":1341},[656],[583,3153,2572],{"className":3154},[661],[583,3156,633],{"className":3157},[759],[583,3159],{"className":3160,"style":1983},[763],[583,3162,1908],{"className":3163},[1987],[583,3165],{"className":3166,"style":1983},[763],[583,3168,3170,3173,3176,3179,3182],{"className":3169},[652],[583,3171],{"className":3172,"style":778},[656],[583,3174,630],{"className":3175},[661],[583,3177],{"className":3178,"style":764},[763],[583,3180,636],{"className":3181},[768],[583,3183],{"className":3184,"style":764},[763],[583,3186,3188,3191,3194,3197,3200,3203,3206],{"className":3187},[652],[583,3189],{"className":3190,"style":2317},[656],[583,3192,1896],{"className":3193},[661],[583,3195,1603],{"className":3196},[661],[583,3198,626],{"className":3199},[661,665],[583,3201],{"className":3202,"style":1983},[763],[583,3204,1908],{"className":3205},[1987],[583,3207],{"className":3208,"style":1983},[763],[583,3210,3212,3215],{"className":3211},[652],[583,3213],{"className":3214,"style":778},[656],[583,3216,1603],{"className":3217},[661],[564,3219,3220,3221,1399,3317,2210,3416,2342,3519,3624],{},"Bei ",[583,3222,3224,3252],{"className":3223},[586],[583,3225,3227],{"className":3226},[590],[592,3228,3229],{"xmlns":594},[596,3230,3231,3249],{},[599,3232,3233,3235,3237,3239,3241,3243],{},[605,3234,607],{},[611,3236,620],{"stretchy":619},[605,3238,626],{},[611,3240,633],{"stretchy":619},[611,3242,636],{},[602,3244,3245,3247],{},[605,3246,626],{},[628,3248,1603],{},[640,3250,3251],{"encoding":642},"f(x) = x^3",[583,3253,3255,3282],{"className":3254,"ariaHidden":648},[647],[583,3256,3258,3261,3264,3267,3270,3273,3276,3279],{"className":3257},[652],[583,3259],{"className":3260,"style":1341},[656],[583,3262,607],{"className":3263,"style":666},[661,665],[583,3265,620],{"className":3266},[709],[583,3268,626],{"className":3269},[661,665],[583,3271,633],{"className":3272},[759],[583,3274],{"className":3275,"style":764},[763],[583,3277,636],{"className":3278},[768],[583,3280],{"className":3281,"style":764},[763],[583,3283,3285,3288],{"className":3284},[652],[583,3286],{"className":3287,"style":1369},[656],[583,3289,3291,3294],{"className":3290},[661],[583,3292,626],{"className":3293},[661,665],[583,3295,3297],{"className":3296},[670],[583,3298,3300],{"className":3299},[674],[583,3301,3303],{"className":3302},[678],[583,3304,3306],{"className":3305,"style":1369},[682],[583,3307,3308,3311],{"style":686},[583,3309],{"className":3310,"style":691},[690],[583,3312,3314],{"className":3313},[695,696,697,698],[583,3315,1603],{"className":3316},[661,698],[583,3318,3320,3348],{"className":3319},[586],[583,3321,3323],{"className":3322},[590],[592,3324,3325],{"xmlns":594},[596,3326,3327,3345],{},[599,3328,3329,3335,3337,3339,3341,3343],{},[602,3330,3331,3333],{},[605,3332,607],{},[611,3334,614],{"mathvariant":613,"lspace":1726,"rspace":1726},[611,3336,620],{"stretchy":619},[628,3338,630],{},[611,3340,633],{"stretchy":619},[611,3342,636],{},[628,3344,630],{},[640,3346,3347],{"encoding":642},"f'(0) = 0",[583,3349,3351,3407],{"className":3350,"ariaHidden":648},[647],[583,3352,3354,3357,3389,3392,3395,3398,3401,3404],{"className":3353},[652],[583,3355],{"className":3356,"style":657},[656],[583,3358,3360,3363],{"className":3359},[661],[583,3361,607],{"className":3362,"style":666},[661,665],[583,3364,3366],{"className":3365},[670],[583,3367,3369],{"className":3368},[674],[583,3370,3372],{"className":3371},[678],[583,3373,3375],{"className":3374,"style":683},[682],[583,3376,3377,3380],{"style":686},[583,3378],{"className":3379,"style":691},[690],[583,3381,3383],{"className":3382},[695,696,697,698],[583,3384,3386],{"className":3385},[661,698],[583,3387,614],{"className":3388},[661,698],[583,3390,620],{"className":3391},[709],[583,3393,630],{"className":3394},[661],[583,3396,633],{"className":3397},[759],[583,3399],{"className":3400,"style":764},[763],[583,3402,636],{"className":3403},[768],[583,3405],{"className":3406,"style":764},[763],[583,3408,3410,3413],{"className":3409},[652],[583,3411],{"className":3412,"style":778},[656],[583,3414,630],{"className":3415},[661],[583,3417,3419,3451],{"className":3418},[586],[583,3420,3422],{"className":3421},[590],[592,3423,3424],{"xmlns":594},[596,3425,3426,3448],{},[599,3427,3428,3438,3440,3442,3444,3446],{},[602,3429,3430,3432],{},[605,3431,607],{},[599,3433,3434,3436],{},[611,3435,614],{"mathvariant":613},[611,3437,614],{"mathvariant":613},[611,3439,620],{"stretchy":619},[628,3441,630],{},[611,3443,633],{"stretchy":619},[611,3445,636],{},[628,3447,630],{},[640,3449,3450],{"encoding":642},"f''(0) = 0",[583,3452,3454,3510],{"className":3453,"ariaHidden":648},[647],[583,3455,3457,3460,3492,3495,3498,3501,3504,3507],{"className":3456},[652],[583,3458],{"className":3459,"style":657},[656],[583,3461,3463,3466],{"className":3462},[661],[583,3464,607],{"className":3465,"style":666},[661,665],[583,3467,3469],{"className":3468},[670],[583,3470,3472],{"className":3471},[674],[583,3473,3475],{"className":3474},[678],[583,3476,3478],{"className":3477,"style":683},[682],[583,3479,3480,3483],{"style":686},[583,3481],{"className":3482,"style":691},[690],[583,3484,3486],{"className":3485},[695,696,697,698],[583,3487,3489],{"className":3488},[661,698],[583,3490,705],{"className":3491},[661,698],[583,3493,620],{"className":3494},[709],[583,3496,630],{"className":3497},[661],[583,3499,633],{"className":3500},[759],[583,3502],{"className":3503,"style":764},[763],[583,3505,636],{"className":3506},[768],[583,3508],{"className":3509,"style":764},[763],[583,3511,3513,3516],{"className":3512},[652],[583,3514],{"className":3515,"style":778},[656],[583,3517,630],{"className":3518},[661],[583,3520,3522,3556],{"className":3521},[586],[583,3523,3525],{"className":3524},[590],[592,3526,3527],{"xmlns":594},[596,3528,3529,3553],{},[599,3530,3531,3543,3545,3547,3549,3551],{},[602,3532,3533,3535],{},[605,3534,607],{},[599,3536,3537,3539,3541],{},[611,3538,614],{"mathvariant":613},[611,3540,614],{"mathvariant":613},[611,3542,614],{"mathvariant":613},[611,3544,620],{"stretchy":619},[628,3546,630],{},[611,3548,633],{"stretchy":619},[611,3550,636],{},[628,3552,2086],{},[640,3554,3555],{"encoding":642},"f'''(0) = 6",[583,3557,3559,3615],{"className":3558,"ariaHidden":648},[647],[583,3560,3562,3565,3597,3600,3603,3606,3609,3612],{"className":3561},[652],[583,3563],{"className":3564,"style":657},[656],[583,3566,3568,3571],{"className":3567},[661],[583,3569,607],{"className":3570,"style":666},[661,665],[583,3572,3574],{"className":3573},[670],[583,3575,3577],{"className":3576},[674],[583,3578,3580],{"className":3579},[678],[583,3581,3583],{"className":3582,"style":683},[682],[583,3584,3585,3588],{"style":686},[583,3586],{"className":3587,"style":691},[690],[583,3589,3591],{"className":3590},[695,696,697,698],[583,3592,3594],{"className":3593},[661,698],[583,3595,872],{"className":3596},[661,698],[583,3598,620],{"className":3599},[709],[583,3601,630],{"className":3602},[661],[583,3604,633],{"className":3605},[759],[583,3607],{"className":3608,"style":764},[763],[583,3610,636],{"className":3611},[768],[583,3613],{"className":3614,"style":764},[763],[583,3616,3618,3621],{"className":3617},[652],[583,3619],{"className":3620,"style":778},[656],[583,3622,2086],{"className":3623},[661],". Der Ursprung ist also ein Sattelpunkt.",[559,3626,3628],{"id":3627},"typische-fehler","Typische Fehler",[573,3630,3631,4118,4422],{},[576,3632,3633,3634,3777,3778,1399,3875,3977,3978,4117],{},"Nur ",[583,3635,3637,3672],{"className":3636},[586],[583,3638,3640],{"className":3639},[590],[592,3641,3642],{"xmlns":594},[596,3643,3644,3670],{},[599,3645,3646,3656,3658,3664,3666,3668],{},[602,3647,3648,3650],{},[605,3649,607],{},[599,3651,3652,3654],{},[611,3653,614],{"mathvariant":613},[611,3655,614],{"mathvariant":613},[611,3657,620],{"stretchy":619},[622,3659,3660,3662],{},[605,3661,626],{},[628,3663,630],{},[611,3665,633],{"stretchy":619},[611,3667,636],{},[628,3669,630],{},[640,3671,643],{"encoding":642},[583,3673,3675,3768],{"className":3674,"ariaHidden":648},[647],[583,3676,3678,3681,3713,3716,3756,3759,3762,3765],{"className":3677},[652],[583,3679],{"className":3680,"style":657},[656],[583,3682,3684,3687],{"className":3683},[661],[583,3685,607],{"className":3686,"style":666},[661,665],[583,3688,3690],{"className":3689},[670],[583,3691,3693],{"className":3692},[674],[583,3694,3696],{"className":3695},[678],[583,3697,3699],{"className":3698,"style":683},[682],[583,3700,3701,3704],{"style":686},[583,3702],{"className":3703,"style":691},[690],[583,3705,3707],{"className":3706},[695,696,697,698],[583,3708,3710],{"className":3709},[661,698],[583,3711,705],{"className":3712},[661,698],[583,3714,620],{"className":3715},[709],[583,3717,3719,3722],{"className":3718},[661],[583,3720,626],{"className":3721},[661,665],[583,3723,3725],{"className":3724},[670],[583,3726,3728,3748],{"className":3727},[674,722],[583,3729,3731,3745],{"className":3730},[678],[583,3732,3734],{"className":3733,"style":729},[682],[583,3735,3736,3739],{"style":732},[583,3737],{"className":3738,"style":691},[690],[583,3740,3742],{"className":3741},[695,696,697,698],[583,3743,630],{"className":3744},[661,698],[583,3746,746],{"className":3747},[745],[583,3749,3751],{"className":3750},[678],[583,3752,3754],{"className":3753,"style":753},[682],[583,3755],{},[583,3757,633],{"className":3758},[759],[583,3760],{"className":3761,"style":764},[763],[583,3763,636],{"className":3764},[768],[583,3766],{"className":3767,"style":764},[763],[583,3769,3771,3774],{"className":3770},[652],[583,3772],{"className":3773,"style":778},[656],[583,3775,630],{"className":3776},[661]," prüfen. Bei ",[583,3779,3781,3810],{"className":3780},[586],[583,3782,3784],{"className":3783},[590],[592,3785,3786],{"xmlns":594},[596,3787,3788,3807],{},[599,3789,3790,3792,3794,3796,3798,3800],{},[605,3791,607],{},[611,3793,620],{"stretchy":619},[605,3795,626],{},[611,3797,633],{"stretchy":619},[611,3799,636],{},[602,3801,3802,3804],{},[605,3803,626],{},[628,3805,3806],{},"4",[640,3808,3809],{"encoding":642},"f(x) = 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aber ",[583,3979,3981,4020],{"className":3980},[586],[583,3982,3984],{"className":3983},[590],[592,3985,3986],{"xmlns":594},[596,3987,3988,4017],{},[599,3989,3990,4000,4002,4004,4006,4008,4011],{},[602,3991,3992,3994],{},[605,3993,607],{},[599,3995,3996,3998],{},[611,3997,614],{"mathvariant":613},[611,3999,614],{"mathvariant":613},[611,4001,620],{"stretchy":619},[605,4003,626],{},[611,4005,633],{"stretchy":619},[611,4007,636],{},[628,4009,4010],{},"12",[602,4012,4013,4015],{},[605,4014,626],{},[628,4016,1905],{},[640,4018,4019],{"encoding":642},"f''(x) = 12x^2",[583,4021,4023,4079],{"className":4022,"ariaHidden":648},[647],[583,4024,4026,4029,4061,4064,4067,4070,4073,4076],{"className":4025},[652],[583,4027],{"className":4028,"style":657},[656],[583,4030,4032,4035],{"className":4031},[661],[583,4033,607],{"className":4034,"style":666},[661,665],[583,4036,4038],{"className":4037},[670],[583,4039,4041],{"className":4040},[674],[583,4042,4044],{"className":4043},[678],[583,4045,4047],{"className":4046,"style":683},[682],[583,4048,4049,4052],{"style":686},[583,4050],{"className":4051,"style":691},[690],[583,4053,4055],{"className":4054},[695,696,697,698],[583,4056,4058],{"className":4057},[661,698],[583,4059,705],{"className":4060},[661,698],[583,4062,620],{"className":4063},[709],[583,4065,626],{"className":4066},[661,665],[583,4068,633],{"className":4069},[759],[583,4071],{"className":4072,"style":764},[763],[583,4074,636],{"className":4075},[768],[583,4077],{"className":4078,"style":764},[763],[583,4080,4082,4085,4088],{"className":4081},[652],[583,4083],{"className":4084,"style":1369},[656],[583,4086,4010],{"className":4087},[661],[583,4089,4091,4094],{"className":4090},[661],[583,4092,626],{"className":4093},[661,665],[583,4095,4097],{"className":4096},[670],[583,4098,4100],{"className":4099},[674],[583,4101,4103],{"className":4102},[678],[583,4104,4106],{"className":4105,"style":1369},[682],[583,4107,4108,4111],{"style":686},[583,4109],{"className":4110,"style":691},[690],[583,4112,4114],{"className":4113},[695,696,697,698],[583,4115,1905],{"className":4116},[661,698]," wechselt das Vorzeichen nicht, es gibt keinen Wendepunkt.",[576,4119,4120,4121,4267,4268,4333,4334,1534,4393,4421],{},"Aus ",[583,4122,4124,4162],{"className":4123},[586],[583,4125,4127],{"className":4126},[590],[592,4128,4129],{"xmlns":594},[596,4130,4131,4159],{},[599,4132,4133,4145,4147,4153,4155,4157],{},[602,4134,4135,4137],{},[605,4136,607],{},[599,4138,4139,4141,4143],{},[611,4140,614],{"mathvariant":613},[611,4142,614],{"mathvariant":613},[611,4144,614],{"mathvariant":613},[611,4146,620],{"stretchy":619},[622,4148,4149,4151],{},[605,4150,626],{},[628,4152,630],{},[611,4154,633],{"stretchy":619},[611,4156,636],{},[628,4158,630],{},[640,4160,4161],{"encoding":642},"f'''(x_0) = 0",[583,4163,4165,4258],{"className":4164,"ariaHidden":648},[647],[583,4166,4168,4171,4203,4206,4246,4249,4252,4255],{"className":4167},[652],[583,4169],{"className":4170,"style":657},[656],[583,4172,4174,4177],{"className":4173},[661],[583,4175,607],{"className":4176,"style":666},[661,665],[583,4178,4180],{"className":4179},[670],[583,4181,4183],{"className":4182},[674],[583,4184,4186],{"className":4185},[678],[583,4187,4189],{"className":4188,"style":683},[682],[583,4190,4191,4194],{"style":686},[583,4192],{"className":4193,"style":691},[690],[583,4195,4197],{"className":4196},[695,696,697,698],[583,4198,4200],{"className":4199},[661,698],[583,4201,872],{"className":4202},[661,698],[583,4204,620],{"className":4205},[709],[583,4207,4209,4212],{"className":4208},[661],[583,4210,626],{"className":4211},[661,665],[583,4213,4215],{"className":4214},[670],[583,4216,4218,4238],{"className":4217},[674,722],[583,4219,4221,4235],{"className":4220},[678],[583,4222,4224],{"className":4223,"style":729},[682],[583,4225,4226,4229],{"style":732},[583,4227],{"className":4228,"style":691},[690],[583,4230,4232],{"className":4231},[695,696,697,698],[583,4233,630],{"className":4234},[661,698],[583,4236,746],{"className":4237},[745],[583,4239,4241],{"className":4240},[678],[583,4242,4244],{"className":4243,"style":753},[682],[583,4245],{},[583,4247,633],{"className":4248},[759],[583,4250],{"className":4251,"style":764},[763],[583,4253,636],{"className":4254},[768],[583,4256],{"className":4257,"style":764},[763],[583,4259,4261,4264],{"className":4260},[652],[583,4262],{"className":4263,"style":778},[656],[583,4265,630],{"className":4266},[661]," schließen, dass keine Wendestelle vorliegt. Dann muss man den Vorzeichenwechsel von ",[583,4269,4271,4292],{"className":4270},[586],[583,4272,4274],{"className":4273},[590],[592,4275,4276],{"xmlns":594},[596,4277,4278,4290],{},[599,4279,4280],{},[602,4281,4282,4284],{},[605,4283,607],{},[599,4285,4286,4288],{},[611,4287,614],{"mathvariant":613},[611,4289,614],{"mathvariant":613},[640,4291,1003],{"encoding":642},[583,4293,4295],{"className":4294,"ariaHidden":648},[647],[583,4296,4298,4301],{"className":4297},[652],[583,4299],{"className":4300,"style":1013},[656],[583,4302,4304,4307],{"className":4303},[661],[583,4305,607],{"className":4306,"style":666},[661,665],[583,4308,4310],{"className":4309},[670],[583,4311,4313],{"className":4312},[674],[583,4314,4316],{"className":4315},[678],[583,4317,4319],{"className":4318,"style":683},[682],[583,4320,4321,4324],{"style":686},[583,4322],{"className":4323,"style":691},[690],[583,4325,4327],{"className":4326},[695,696,697,698],[583,4328,4330],{"className":4329},[661,698],[583,4331,705],{"className":4332},[661,698]," prüfen, z.B. hat ",[583,4335,4337,4355],{"className":4336},[586],[583,4338,4340],{"className":4339},[590],[592,4341,4342],{"xmlns":594},[596,4343,4344,4352],{},[599,4345,4346],{},[602,4347,4348,4350],{},[605,4349,626],{},[628,4351,1328],{},[640,4353,4354],{"encoding":642},"x^5",[583,4356,4358],{"className":4357,"ariaHidden":648},[647],[583,4359,4361,4364],{"className":4360},[652],[583,4362],{"className":4363,"style":1369},[656],[583,4365,4367,4370],{"className":4366},[661],[583,4368,626],{"className":4369},[661,665],[583,4371,4373],{"className":4372},[670],[583,4374,4376],{"className":4375},[674],[583,4377,4379],{"className":4378},[678],[583,4380,4382],{"className":4381,"style":1369},[682],[583,4383,4384,4387],{"style":686},[583,4385],{"className":4386,"style":691},[690],[583,4388,4390],{"className":4389},[695,696,697,698],[583,4391,1328],{"className":4392},[661,698],[583,4394,4396,4409],{"className":4395},[586],[583,4397,4399],{"className":4398},[590],[592,4400,4401],{"xmlns":594},[596,4402,4403,4407],{},[599,4404,4405],{},[628,4406,630],{},[640,4408,630],{"encoding":642},[583,4410,4412],{"className":4411,"ariaHidden":648},[647],[583,4413,4415,4418],{"className":4414},[652],[583,4416],{"className":4417,"style":778},[656],[583,4419,630],{"className":4420},[661]," einen Wendepunkt.",[576,4423,4424,4425,4487,4488,782],{},"Wendestelle und Extremstelle verwechseln. Für Extremstellen ist ",[583,4426,4428,4446],{"className":4427},[586],[583,4429,4431],{"className":4430},[590],[592,4432,4433],{"xmlns":594},[596,4434,4435,4443],{},[599,4436,4437],{},[602,4438,4439,4441],{},[605,4440,607],{},[611,4442,614],{"mathvariant":613,"lspace":1726,"rspace":1726},[640,4444,4445],{"encoding":642},"f'",[583,4447,4449],{"className":4448,"ariaHidden":648},[647],[583,4450,4452,4455],{"className":4451},[652],[583,4453],{"className":4454,"style":1013},[656],[583,4456,4458,4461],{"className":4457},[661],[583,4459,607],{"className":4460,"style":666},[661,665],[583,4462,4464],{"className":4463},[670],[583,4465,4467],{"className":4466},[674],[583,4468,4470],{"className":4469},[678],[583,4471,4473],{"className":4472,"style":683},[682],[583,4474,4475,4478],{"style":686},[583,4476],{"className":4477,"style":691},[690],[583,4479,4481],{"className":4480},[695,696,697,698],[583,4482,4484],{"className":4483},[661,698],[583,4485,614],{"className":4486},[661,698]," null, für Wendestellen 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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:0.6444em;\">\u003C\u002Fspan>\u003Cspan 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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\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\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=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8444em;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:0.3011em;\">\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=\"mord text\">\u003Cspan class=\"mord\"> ist Wendestelle\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},"\u002Fde\u002Fformulas\u002Fmath\u002Fcalculus\u002Fbedingungen-wendestellen",[],[4634,4635,4636],"extremum-condition","tangent-line","inflection-tangent",{"title":548,"description":4554},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fbedingungen-wendestellen","Ist die zweite Ableitung null und die dritte ungleich null, wechselt der Graph dort seine 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