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Folgerungen:",[1146,1147,1148,1267,1469],"ul",{},[1149,1150,1151,1152,1237,1238,1266],"li",{},"Ist ",[572,1153,1155,1177],{"className":1154},[575],[572,1156,1158],{"className":1157},[579],[581,1159,1160],{"xmlns":583},[585,1161,1162,1174],{},[588,1163,1164,1170,1172],{},[1035,1165,1166,1168],{},[591,1167,673],{},[662,1169,1043],{"mathvariant":1041,"lspace":1042,"rspace":1042},[662,1171,879],{},[1053,1173,1055],{},[595,1175,1176],{"encoding":597},"f' = 0",[572,1178,1180,1228],{"className":1179,"ariaHidden":602},[601],[572,1181,1183,1187,1219,1222,1225],{"className":1182},[606],[572,1184],{"className":1185,"style":1186},[610],"height:0.9463em;vertical-align:-0.1944em;",[572,1188,1190,1193],{"className":1189},[615],[572,1191,673],{"className":1192,"style":724},[615,616],[572,1194,1196],{"className":1195},[1078],[572,1197,1199],{"className":1198},[1082],[572,1200,1202],{"className":1201},[1086],[572,1203,1205],{"className":1204,"style":1091},[1090],[572,1206,1207,1210],{"style":1094},[572,1208],{"className":1209,"style":1099},[1098],[572,1211,1213],{"className":1212},[1103,1104,1105,1106],[572,1214,1216],{"className":1215},[615,1106],[572,1217,1043],{"className":1218},[615,1106],[572,1220],{"className":1221,"style":707},[706],[572,1223,879],{"className":1224},[711],[572,1226],{"className":1227,"style":707},[706],[572,1229,1231,1234],{"className":1230},[606],[572,1232],{"className":1233,"style":1137},[610],[572,1235,1055],{"className":1236},[615]," auf einem Intervall, ist ",[572,1239,1241,1254],{"className":1240},[575],[572,1242,1244],{"className":1243},[579],[581,1245,1246],{"xmlns":583},[585,1247,1248,1252],{},[588,1249,1250],{},[591,1251,673],{},[595,1253,673],{"encoding":597},[572,1255,1257],{"className":1256,"ariaHidden":602},[601],[572,1258,1260,1263],{"className":1259},[606],[572,1261],{"className":1262,"style":848},[610],[572,1264,673],{"className":1265,"style":724},[615,616]," dort konstant.",[1149,1268,1151,1269,1237,1354,1382,1383,1468],{},[572,1270,1272,1295],{"className":1271},[575],[572,1273,1275],{"className":1274},[579],[581,1276,1277],{"xmlns":583},[585,1278,1279,1292],{},[588,1280,1281,1287,1290],{},[1035,1282,1283,1285],{},[591,1284,673],{},[662,1286,1043],{"mathvariant":1041,"lspace":1042,"rspace":1042},[662,1288,1289],{},">",[1053,1291,1055],{},[595,1293,1294],{"encoding":597},"f' > 0",[572,1296,1298,1345],{"className":1297,"ariaHidden":602},[601],[572,1299,1301,1304,1336,1339,1342],{"className":1300},[606],[572,1302],{"className":1303,"style":1186},[610],[572,1305,1307,1310],{"className":1306},[615],[572,1308,673],{"className":1309,"style":724},[615,616],[572,1311,1313],{"className":1312},[1078],[572,1314,1316],{"className":1315},[1082],[572,1317,1319],{"className":1318},[1086],[572,1320,1322],{"className":1321,"style":1091},[1090],[572,1323,1324,1327],{"style":1094},[572,1325],{"className":1326,"style":1099},[1098],[572,1328,1330],{"className":1329},[1103,1104,1105,1106],[572,1331,1333],{"className":1332},[615,1106],[572,1334,1043],{"className":1335},[615,1106],[572,1337],{"className":1338,"style":707},[706],[572,1340,1289],{"className":1341},[711],[572,1343],{"className":1344,"style":707},[706],[572,1346,1348,1351],{"className":1347},[606],[572,1349],{"className":1350,"style":1137},[610],[572,1352,1055],{"className":1353},[615],[572,1355,1357,1370],{"className":1356},[575],[572,1358,1360],{"className":1359},[579],[581,1361,1362],{"xmlns":583},[585,1363,1364,1368],{},[588,1365,1366],{},[591,1367,673],{},[595,1369,673],{"encoding":597},[572,1371,1373],{"className":1372,"ariaHidden":602},[601],[572,1374,1376,1379],{"className":1375},[606],[572,1377],{"className":1378,"style":848},[610],[572,1380,673],{"className":1381,"style":724},[615,616]," dort streng monoton wachsend (entsprechend fallend für ",[572,1384,1386,1409],{"className":1385},[575],[572,1387,1389],{"className":1388},[579],[581,1390,1391],{"xmlns":583},[585,1392,1393,1406],{},[588,1394,1395,1401,1404],{},[1035,1396,1397,1399],{},[591,1398,673],{},[662,1400,1043],{"mathvariant":1041,"lspace":1042,"rspace":1042},[662,1402,1403],{},"\u003C",[1053,1405,1055],{},[595,1407,1408],{"encoding":597},"f' \u003C 0",[572,1410,1412,1459],{"className":1411,"ariaHidden":602},[601],[572,1413,1415,1418,1450,1453,1456],{"className":1414},[606],[572,1416],{"className":1417,"style":1186},[610],[572,1419,1421,1424],{"className":1420},[615],[572,1422,673],{"className":1423,"style":724},[615,616],[572,1425,1427],{"className":1426},[1078],[572,1428,1430],{"className":1429},[1082],[572,1431,1433],{"className":1432},[1086],[572,1434,1436],{"className":1435,"style":1091},[1090],[572,1437,1438,1441],{"style":1094},[572,1439],{"className":1440,"style":1099},[1098],[572,1442,1444],{"className":1443},[1103,1104,1105,1106],[572,1445,1447],{"className":1446},[615,1106],[572,1448,1043],{"className":1449},[615,1106],[572,1451],{"className":1452,"style":707},[706],[572,1454,1403],{"className":1455},[711],[572,1457],{"className":1458,"style":707},[706],[572,1460,1462,1465],{"className":1461},[606],[572,1463],{"className":1464,"style":1137},[610],[572,1466,1055],{"className":1467},[615],").",[1149,1470,1151,1471,1568,1569,1740,1741,1820,1821,1141],{},[572,1472,1474,1502],{"className":1473},[575],[572,1475,1477],{"className":1476},[579],[581,1478,1479],{"xmlns":583},[585,1480,1481,1499],{},[588,1482,1483,1485,1491,1493,1496],{},[591,1484,670],{"mathvariant":1041},[1035,1486,1487,1489],{},[591,1488,673],{},[662,1490,1043],{"mathvariant":1041,"lspace":1042,"rspace":1042},[591,1492,670],{"mathvariant":1041},[662,1494,1495],{},"≤",[591,1497,1498],{},"L",[595,1500,1501],{"encoding":597},"|f'| \\leq L",[572,1503,1505,1558],{"className":1504,"ariaHidden":602},[601],[572,1506,1508,1511,1514,1546,1549,1552,1555],{"className":1507},[606],[572,1509],{"className":1510,"style":1068},[610],[572,1512,670],{"className":1513},[615],[572,1515,1517,1520],{"className":1516},[615],[572,1518,673],{"className":1519,"style":724},[615,616],[572,1521,1523],{"className":1522},[1078],[572,1524,1526],{"className":1525},[1082],[572,1527,1529],{"className":1528},[1086],[572,1530,1532],{"className":1531,"style":1091},[1090],[572,1533,1534,1537],{"style":1094},[572,1535],{"className":1536,"style":1099},[1098],[572,1538,1540],{"className":1539},[1103,1104,1105,1106],[572,1541,1543],{"className":1542},[615,1106],[572,1544,1043],{"className":1545},[615,1106],[572,1547,670],{"className":1548},[615],[572,1550],{"className":1551,"style":707},[706],[572,1553,1495],{"className":1554},[711],[572,1556],{"className":1557,"style":707},[706],[572,1559,1561,1565],{"className":1560},[606],[572,1562],{"className":1563,"style":1564},[610],"height:0.6833em;",[572,1566,1498],{"className":1567},[615,616],", gilt die Abschätzung ",[572,1570,1572,1624],{"className":1571},[575],[572,1573,1575],{"className":1574},[579],[581,1576,1577],{"xmlns":583},[585,1578,1579,1621],{},[588,1580,1581,1583,1585,1587,1589,1591,1594,1596,1598,1600,1602,1604,1606,1608,1611,1613,1615,1617,1619],{},[591,1582,670],{"mathvariant":1041},[591,1584,673],{},[662,1586,665],{"stretchy":664},[591,1588,632],{},[662,1590,680],{"stretchy":664},[662,1592,1593],{},"−",[591,1595,673],{},[662,1597,665],{"stretchy":664},[591,1599,593],{},[662,1601,680],{"stretchy":664},[591,1603,670],{"mathvariant":1041},[662,1605,1495],{},[591,1607,1498],{},[662,1609,1610],{},"⋅",[591,1612,670],{"mathvariant":1041},[591,1614,632],{},[662,1616,1593],{},[591,1618,593],{},[591,1620,670],{"mathvariant":1041},[595,1622,1623],{"encoding":597},"|f(b) - f(a)| \\leq L \\cdot |b - a|",[572,1625,1627,1659,1689,1707,1728],{"className":1626,"ariaHidden":602},[601],[572,1628,1630,1633,1636,1639,1642,1645,1648,1652,1656],{"className":1629},[606],[572,1631],{"className":1632,"style":695},[610],[572,1634,670],{"className":1635},[615],[572,1637,673],{"className":1638,"style":724},[615,616],[572,1640,665],{"className":1641},[699],[572,1643,632],{"className":1644},[615,616],[572,1646,680],{"className":1647},[734],[572,1649],{"className":1650,"style":1651},[706],"margin-right:0.2222em;",[572,1653,1593],{"className":1654},[1655],"mbin",[572,1657],{"className":1658,"style":1651},[706],[572,1660,1662,1665,1668,1671,1674,1677,1680,1683,1686],{"className":1661},[606],[572,1663],{"className":1664,"style":695},[610],[572,1666,673],{"className":1667,"style":724},[615,616],[572,1669,665],{"className":1670},[699],[572,1672,593],{"className":1673},[615,616],[572,1675,680],{"className":1676},[734],[572,1678,670],{"className":1679},[615],[572,1681],{"className":1682,"style":707},[706],[572,1684,1495],{"className":1685},[711],[572,1687],{"className":1688,"style":707},[706],[572,1690,1692,1695,1698,1701,1704],{"className":1691},[606],[572,1693],{"className":1694,"style":1564},[610],[572,1696,1498],{"className":1697},[615,616],[572,1699],{"className":1700,"style":1651},[706],[572,1702,1610],{"className":1703},[1655],[572,1705],{"className":1706,"style":1651},[706],[572,1708,1710,1713,1716,1719,1722,1725],{"className":1709},[606],[572,1711],{"className":1712,"style":695},[610],[572,1714,670],{"className":1715},[615],[572,1717,632],{"className":1718},[615,616],[572,1720],{"className":1721,"style":1651},[706],[572,1723,1593],{"className":1724},[1655],[572,1726],{"className":1727,"style":1651},[706],[572,1729,1731,1734,1737],{"className":1730},[606],[572,1732],{"className":1733,"style":695},[610],[572,1735,593],{"className":1736},[615,616],[572,1738,670],{"className":1739},[615],". Wegen ",[572,1742,1744,1774],{"className":1743},[575],[572,1745,1747],{"className":1746},[579],[581,1748,1749],{"xmlns":583},[585,1750,1751,1771],{},[588,1752,1753,1755,1758,1761,1764,1766,1768],{},[591,1754,670],{"mathvariant":1041},[591,1756,1757],{},"cos",[662,1759,1760],{},"⁡",[591,1762,1763],{},"x",[591,1765,670],{"mathvariant":1041},[662,1767,1495],{},[1053,1769,1770],{},"1",[595,1772,1773],{"encoding":597},"|\\cos x| \\leq 1",[572,1775,1777,1811],{"className":1776,"ariaHidden":602},[601],[572,1778,1780,1783,1786,1789,1793,1796,1799,1802,1805,1808],{"className":1779},[606],[572,1781],{"className":1782,"style":695},[610],[572,1784,670],{"className":1785},[615],[572,1787],{"className":1788,"style":1014},[706],[572,1790,1757],{"className":1791},[1792],"mop",[572,1794],{"className":1795,"style":1014},[706],[572,1797,1763],{"className":1798},[615,616],[572,1800,670],{"className":1801},[615],[572,1803],{"className":1804,"style":707},[706],[572,1806,1495],{"className":1807},[711],[572,1809],{"className":1810,"style":707},[706],[572,1812,1814,1817],{"className":1813},[606],[572,1815],{"className":1816,"style":1137},[610],[572,1818,1770],{"className":1819},[615]," ist z.B. ",[572,1822,1824,1867],{"className":1823},[575],[572,1825,1827],{"className":1826},[579],[581,1828,1829],{"xmlns":583},[585,1830,1831,1864],{},[588,1832,1833,1835,1838,1840,1842,1844,1846,1848,1850,1852,1854,1856,1858,1860,1862],{},[591,1834,670],{"mathvariant":1041},[591,1836,1837],{},"sin",[662,1839,1760],{},[591,1841,632],{},[662,1843,1593],{},[591,1845,1837],{},[662,1847,1760],{},[591,1849,593],{},[591,1851,670],{"mathvariant":1041},[662,1853,1495],{},[591,1855,670],{"mathvariant":1041},[591,1857,632],{},[662,1859,1593],{},[591,1861,593],{},[591,1863,670],{"mathvariant":1041},[595,1865,1866],{"encoding":597},"|\\sin b - \\sin a| \\leq |b - a|",[572,1868,1870,1900,1927,1948],{"className":1869,"ariaHidden":602},[601],[572,1871,1873,1876,1879,1882,1885,1888,1891,1894,1897],{"className":1872},[606],[572,1874],{"className":1875,"style":695},[610],[572,1877,670],{"className":1878},[615],[572,1880],{"className":1881,"style":1014},[706],[572,1883,1837],{"className":1884},[1792],[572,1886],{"className":1887,"style":1014},[706],[572,1889,632],{"className":1890},[615,616],[572,1892],{"className":1893,"style":1651},[706],[572,1895,1593],{"className":1896},[1655],[572,1898],{"className":1899,"style":1651},[706],[572,1901,1903,1906,1909,1912,1915,1918,1921,1924],{"className":1902},[606],[572,1904],{"className":1905,"style":695},[610],[572,1907,1837],{"className":1908},[1792],[572,1910],{"className":1911,"style":1014},[706],[572,1913,593],{"className":1914},[615,616],[572,1916,670],{"className":1917},[615],[572,1919],{"className":1920,"style":707},[706],[572,1922,1495],{"className":1923},[711],[572,1925],{"className":1926,"style":707},[706],[572,1928,1930,1933,1936,1939,1942,1945],{"className":1929},[606],[572,1931],{"className":1932,"style":695},[610],[572,1934,670],{"className":1935},[615],[572,1937,632],{"className":1938},[615,616],[572,1940],{"className":1941,"style":1651},[706],[572,1943,1593],{"className":1944},[1655],[572,1946],{"className":1947,"style":1651},[706],[572,1949,1951,1954,1957],{"className":1950},[606],[572,1952],{"className":1953,"style":695},[610],[572,1955,593],{"className":1956},[615,616],[572,1958,670],{"className":1959},[615],[559,1961,1963],{"id":1962},"beispiele","Beispiele",[564,1965,1966,2064,2065,2120,2121,2269,2270,2396,2397,1141],{},[572,1967,1969,1998],{"className":1968},[575],[572,1970,1972],{"className":1971},[579],[581,1973,1974],{"xmlns":583},[585,1975,1976,1995],{},[588,1977,1978,1980,1982,1984,1986,1988],{},[591,1979,673],{},[662,1981,665],{"stretchy":664},[591,1983,1763],{},[662,1985,680],{"stretchy":664},[662,1987,879],{},[1035,1989,1990,1992],{},[591,1991,1763],{},[1053,1993,1994],{},"2",[595,1996,1997],{"encoding":597},"f(x) = x^2",[572,1999,2001,2028],{"className":2000,"ariaHidden":602},[601],[572,2002,2004,2007,2010,2013,2016,2019,2022,2025],{"className":2003},[606],[572,2005],{"className":2006,"style":695},[610],[572,2008,673],{"className":2009,"style":724},[615,616],[572,2011,665],{"className":2012},[699],[572,2014,1763],{"className":2015},[615,616],[572,2017,680],{"className":2018},[734],[572,2020],{"className":2021,"style":707},[706],[572,2023,879],{"className":2024},[711],[572,2026],{"className":2027,"style":707},[706],[572,2029,2031,2035],{"className":2030},[606],[572,2032],{"className":2033,"style":2034},[610],"height:0.8141em;",[572,2036,2038,2041],{"className":2037},[615],[572,2039,1763],{"className":2040},[615,616],[572,2042,2044],{"className":2043},[1078],[572,2045,2047],{"className":2046},[1082],[572,2048,2050],{"className":2049},[1086],[572,2051,2053],{"className":2052,"style":2034},[1090],[572,2054,2055,2058],{"style":1094},[572,2056],{"className":2057,"style":1099},[1098],[572,2059,2061],{"className":2060},[1103,1104,1105,1106],[572,2062,1994],{"className":2063},[615,1106]," auf ",[572,2066,2068,2093],{"className":2067},[575],[572,2069,2071],{"className":2070},[579],[581,2072,2073],{"xmlns":583},[585,2074,2075,2090],{},[588,2076,2077,2080,2082,2084,2087],{},[662,2078,2079],{"stretchy":664},"[",[1053,2081,1770],{},[662,2083,966],{"separator":602},[1053,2085,2086],{},"3",[662,2088,2089],{"stretchy":664},"]",[595,2091,2092],{"encoding":597},"[1, 3]",[572,2094,2096],{"className":2095,"ariaHidden":602},[601],[572,2097,2099,2102,2105,2108,2111,2114,2117],{"className":2098},[606],[572,2100],{"className":2101,"style":695},[610],[572,2103,2079],{"className":2104},[699],[572,2106,1770],{"className":2107},[615],[572,2109,966],{"className":2110},[1010],[572,2112],{"className":2113,"style":1014},[706],[572,2115,2086],{"className":2116},[615],[572,2118,2089],{"className":2119},[734],": Die Sekantensteigung ist ",[572,2122,2124,2155],{"className":2123},[575],[572,2125,2127],{"className":2126},[579],[581,2128,2129],{"xmlns":583},[585,2130,2131,2152],{},[588,2132,2133,2147,2149],{},[2134,2135,2136,2145],"mfrac",{},[588,2137,2138,2141,2143],{},[1053,2139,2140],{},"9",[662,2142,1593],{},[1053,2144,1770],{},[1053,2146,1994],{},[662,2148,879],{},[1053,2150,2151],{},"4",[595,2153,2154],{"encoding":597},"\\frac{9 - 1}{2} = 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Aus ",[572,2271,2273,2307],{"className":2272},[575],[572,2274,2276],{"className":2275},[579],[581,2277,2278],{"xmlns":583},[585,2279,2280,2304],{},[588,2281,2282,2288,2290,2292,2294,2296,2298,2300,2302],{},[1035,2283,2284,2286],{},[591,2285,673],{},[662,2287,1043],{"mathvariant":1041,"lspace":1042,"rspace":1042},[662,2289,665],{"stretchy":664},[591,2291,835],{},[662,2293,680],{"stretchy":664},[662,2295,879],{},[1053,2297,1994],{},[591,2299,835],{},[662,2301,879],{},[1053,2303,2151],{},[595,2305,2306],{"encoding":597},"f'(\\xi) = 2\\xi = 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folgt ",[572,2398,2400,2418],{"className":2399},[575],[572,2401,2403],{"className":2402},[579],[581,2404,2405],{"xmlns":583},[585,2406,2407,2415],{},[588,2408,2409,2411,2413],{},[591,2410,835],{},[662,2412,879],{},[1053,2414,1994],{},[595,2416,2417],{"encoding":597},"\\xi = 2",[572,2419,2421,2439],{"className":2420,"ariaHidden":602},[601],[572,2422,2424,2427,2430,2433,2436],{"className":2423},[606],[572,2425],{"className":2426,"style":848},[610],[572,2428,835],{"className":2429,"style":852},[615,616],[572,2431],{"className":2432,"style":707},[706],[572,2434,879],{"className":2435},[711],[572,2437],{"className":2438,"style":707},[706],[572,2440,2442,2445],{"className":2441},[606],[572,2443],{"className":2444,"style":1137},[610],[572,2446,1994],{"className":2447},[615],[564,2449,2450,2064,2546,2120,2598,2269,2731,2396,2818,2969],{},[572,2451,2453,2481],{"className":2452},[575],[572,2454,2456],{"className":2455},[579],[581,2457,2458],{"xmlns":583},[585,2459,2460,2478],{},[588,2461,2462,2464,2466,2468,2470,2472],{},[591,2463,673],{},[662,2465,665],{"stretchy":664},[591,2467,1763],{},[662,2469,680],{"stretchy":664},[662,2471,879],{},[1035,2473,2474,2476],{},[591,2475,1763],{},[1053,2477,2086],{},[595,2479,2480],{"encoding":597},"f(x) = x^3",[572,2482,2484,2511],{"className":2483,"ariaHidden":602},[601],[572,2485,2487,2490,2493,2496,2499,2502,2505,2508],{"className":2486},[606],[572,2488],{"className":2489,"style":695},[610],[572,2491,673],{"className":2492,"style":724},[615,616],[572,2494,665],{"className":2495},[699],[572,2497,1763],{"className":2498},[615,616],[572,2500,680],{"className":2501},[734],[572,2503],{"className":2504,"style":707},[706],[572,2506,879],{"className":2507},[711],[572,2509],{"className":2510,"style":707},[706],[572,2512,2514,2517],{"className":2513},[606],[572,2515],{"className":2516,"style":2034},[610],[572,2518,2520,2523],{"className":2519},[615],[572,2521,1763],{"className":2522},[615,616],[572,2524,2526],{"className":2525},[1078],[572,2527,2529],{"className":2528},[1082],[572,2530,2532],{"className":2531},[1086],[572,2533,2535],{"className":2534,"style":2034},[1090],[572,2536,2537,2540],{"style":1094},[572,2538],{"className":2539,"style":1099},[1098],[572,2541,2543],{"className":2542},[1103,1104,1105,1106],[572,2544,2086],{"className":2545},[615,1106],[572,2547,2549,2571],{"className":2548},[575],[572,2550,2552],{"className":2551},[579],[581,2553,2554],{"xmlns":583},[585,2555,2556,2568],{},[588,2557,2558,2560,2562,2564,2566],{},[662,2559,2079],{"stretchy":664},[1053,2561,1055],{},[662,2563,966],{"separator":602},[1053,2565,2086],{},[662,2567,2089],{"stretchy":664},[595,2569,2570],{"encoding":597},"[0, 3]",[572,2572,2574],{"className":2573,"ariaHidden":602},[601],[572,2575,2577,2580,2583,2586,2589,2592,2595],{"className":2576},[606],[572,2578],{"className":2579,"style":695},[610],[572,2581,2079],{"className":2582},[699],[572,2584,1055],{"className":2585},[615],[572,2587,966],{"className":2588},[1010],[572,2590],{"className":2591,"style":1014},[706],[572,2593,2086],{"className":2594},[615],[572,2596,2089],{"className":2597},[734],[572,2599,2601,2630],{"className":2600},[575],[572,2602,2604],{"className":2603},[579],[581,2605,2606],{"xmlns":583},[585,2607,2608,2627],{},[588,2609,2610,2623,2625],{},[2134,2611,2612,2621],{},[588,2613,2614,2617,2619],{},[1053,2615,2616],{},"27",[662,2618,1593],{},[1053,2620,1055],{},[1053,2622,2086],{},[662,2624,879],{},[1053,2626,2140],{},[595,2628,2629],{"encoding":597},"\\frac{27 - 0}{3} = 9",[572,2631,2633,2722],{"className":2632,"ariaHidden":602},[601],[572,2634,2636,2639,2713,2716,2719],{"className":2635},[606],[572,2637],{"className":2638,"style":2164},[610],[572,2640,2642,2645,2710],{"className":2641},[615],[572,2643],{"className":2644},[699,2171],[572,2646,2648],{"className":2647},[2134],[572,2649,2651,2702],{"className":2650},[1082,2178],[572,2652,2654,2699],{"className":2653},[1086],[572,2655,2657,2671,2679],{"className":2656,"style":2185},[1090],[572,2658,2659,2662],{"style":2188},[572,2660],{"className":2661,"style":2192},[1098],[572,2663,2665],{"className":2664},[1103,1104,1105,1106],[572,2666,2668],{"className":2667},[615,1106],[572,2669,2086],{"className":2670},[615,1106],[572,2672,2673,2676],{"style":2204},[572,2674],{"className":2675,"style":2192},[1098],[572,2677],{"className":2678,"style":2212},[2211],[572,2680,2681,2684],{"style":2215},[572,2682],{"className":2683,"style":2192},[1098],[572,2685,2687],{"className":2686},[1103,1104,1105,1106],[572,2688,2690,2693,2696],{"className":2689},[615,1106],[572,2691,2616],{"className":2692},[615,1106],[572,2694,1593],{"className":2695},[1655,1106],[572,2697,1055],{"className":2698},[615,1106],[572,2700,2238],{"className":2701},[2237],[572,2703,2705],{"className":2704},[1086],[572,2706,2708],{"className":2707,"style":2245},[1090],[572,2709],{},[572,2711],{"className":2712},[734,2171],[572,2714],{"className":2715,"style":707},[706],[572,2717,879],{"className":2718},[711],[572,2720],{"className":2721,"style":707},[706],[572,2723,2725,2728],{"className":2724},[606],[572,2726],{"className":2727,"style":1137},[610],[572,2729,2140],{"className":2730},[615],[572,2732,2734,2758],{"className":2733},[575],[572,2735,2737],{"className":2736},[579],[581,2738,2739],{"xmlns":583},[585,2740,2741,2755],{},[588,2742,2743,2745,2751,2753],{},[1053,2744,2086],{},[1035,2746,2747,2749],{},[591,2748,835],{},[1053,2750,1994],{},[662,2752,879],{},[1053,2754,2140],{},[595,2756,2757],{"encoding":597},"3\\xi^2 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",[572,2980,2982,3010],{"className":2981},[575],[572,2983,2985],{"className":2984},[579],[581,2986,2987],{"xmlns":583},[585,2988,2989,3007],{},[588,2990,2991,2993,2995,2997,2999,3001,3003,3005],{},[591,2992,673],{},[662,2994,665],{"stretchy":664},[591,2996,1763],{},[662,2998,680],{"stretchy":664},[662,3000,879],{},[591,3002,670],{"mathvariant":1041},[591,3004,1763],{},[591,3006,670],{"mathvariant":1041},[595,3008,3009],{"encoding":597},"f(x) = |x|",[572,3011,3013,3040],{"className":3012,"ariaHidden":602},[601],[572,3014,3016,3019,3022,3025,3028,3031,3034,3037],{"className":3015},[606],[572,3017],{"className":3018,"style":695},[610],[572,3020,673],{"className":3021,"style":724},[615,616],[572,3023,665],{"className":3024},[699],[572,3026,1763],{"className":3027},[615,616],[572,3029,680],{"className":3030},[734],[572,3032],{"className":3033,"style":707},[706],[572,3035,879],{"className":3036},[711],[572,3038],{"className":3039,"style":707},[706],[572,3041,3043,3046,3049,3052],{"className":3042},[606],[572,3044],{"className":3045,"style":695},[610],[572,3047,670],{"className":3048},[615],[572,3050,1763],{"className":3051},[615,616],[572,3053,670],{"className":3054},[615],[572,3056,3058,3082],{"className":3057},[575],[572,3059,3061],{"className":3060},[579],[581,3062,3063],{"xmlns":583},[585,3064,3065,3079],{},[588,3066,3067,3069,3071,3073,3075,3077],{},[662,3068,2079],{"stretchy":664},[662,3070,1593],{},[1053,3072,1770],{},[662,3074,966],{"separator":602},[1053,3076,1770],{},[662,3078,2089],{"stretchy":664},[595,3080,3081],{"encoding":597},"[-1, 1]",[572,3083,3085],{"className":3084,"ariaHidden":602},[601],[572,3086,3088,3091,3094,3097,3100,3103,3106,3109],{"className":3087},[606],[572,3089],{"className":3090,"style":695},[610],[572,3092,2079],{"className":3093},[699],[572,3095,1593],{"className":3096},[615],[572,3098,1770],{"className":3099},[615],[572,3101,966],{"className":3102},[1010],[572,3104],{"className":3105,"style":1014},[706],[572,3107,1770],{"className":3108},[615],[572,3110,2089],{"className":3111},[734]," hat die Sekantensteigung ",[572,3114,3116,3129],{"className":3115},[575],[572,3117,3119],{"className":3118},[579],[581,3120,3121],{"xmlns":583},[585,3122,3123,3127],{},[588,3124,3125],{},[1053,3126,1055],{},[595,3128,1055],{"encoding":597},[572,3130,3132],{"className":3131,"ariaHidden":602},[601],[572,3133,3135,3138],{"className":3134},[606],[572,3136],{"className":3137,"style":1137},[610],[572,3139,1055],{"className":3140},[615],", aber ",[572,3143,3145,3163],{"className":3144},[575],[572,3146,3148],{"className":3147},[579],[581,3149,3150],{"xmlns":583},[585,3151,3152,3160],{},[588,3153,3154],{},[1035,3155,3156,3158],{},[591,3157,673],{},[662,3159,1043],{"mathvariant":1041,"lspace":1042,"rspace":1042},[595,3161,3162],{"encoding":597},"f'",[572,3164,3166],{"className":3165,"ariaHidden":602},[601],[572,3167,3169,3172],{"className":3168},[606],[572,3170],{"className":3171,"style":1186},[610],[572,3173,3175,3178],{"className":3174},[615],[572,3176,673],{"className":3177,"style":724},[615,616],[572,3179,3181],{"className":3180},[1078],[572,3182,3184],{"className":3183},[1082],[572,3185,3187],{"className":3186},[1086],[572,3188,3190],{"className":3189,"style":1091},[1090],[572,3191,3192,3195],{"style":1094},[572,3193],{"className":3194,"style":1099},[1098],[572,3196,3198],{"className":3197},[1103,1104,1105,1106],[572,3199,3201],{"className":3200},[615,1106],[572,3202,1043],{"className":3203},[615,1106]," ist nirgends ",[572,3206,3208,3221],{"className":3207},[575],[572,3209,3211],{"className":3210},[579],[581,3212,3213],{"xmlns":583},[585,3214,3215,3219],{},[588,3216,3217],{},[1053,3218,1055],{},[595,3220,1055],{"encoding":597},[572,3222,3224],{"className":3223,"ariaHidden":602},[601],[572,3225,3227,3230],{"className":3226},[606],[572,3228],{"className":3229,"style":1137},[610],[572,3231,1055],{"className":3232},[615],". Der Satz gilt nicht, weil ",[572,3235,3237,3255],{"className":3236},[575],[572,3238,3240],{"className":3239},[579],[581,3241,3242],{"xmlns":583},[585,3243,3244,3252],{},[588,3245,3246,3248,3250],{},[591,3247,670],{"mathvariant":1041},[591,3249,1763],{},[591,3251,670],{"mathvariant":1041},[595,3253,3254],{"encoding":597},"|x|",[572,3256,3258],{"className":3257,"ariaHidden":602},[601],[572,3259,3261,3264,3267,3270],{"className":3260},[606],[572,3262],{"className":3263,"style":695},[610],[572,3265,670],{"className":3266},[615],[572,3268,1763],{"className":3269},[615,616],[572,3271,670],{"className":3272},[615]," bei ",[572,3275,3277,3290],{"className":3276},[575],[572,3278,3280],{"className":3279},[579],[581,3281,3282],{"xmlns":583},[585,3283,3284,3288],{},[588,3285,3286],{},[1053,3287,1055],{},[595,3289,1055],{"encoding":597},[572,3291,3293],{"className":3292,"ariaHidden":602},[601],[572,3294,3296,3299],{"className":3295},[606],[572,3297],{"className":3298,"style":1137},[610],[572,3300,1055],{"className":3301},[615]," nicht differenzierbar ist.",[1149,3304,3305,3306,3334,3335,3432,3433,1141],{},"Annehmen, ",[572,3307,3309,3322],{"className":3308},[575],[572,3310,3312],{"className":3311},[579],[581,3313,3314],{"xmlns":583},[585,3315,3316,3320],{},[588,3317,3318],{},[591,3319,835],{},[595,3321,838],{"encoding":597},[572,3323,3325],{"className":3324,"ariaHidden":602},[601],[572,3326,3328,3331],{"className":3327},[606],[572,3329],{"className":3330,"style":848},[610],[572,3332,835],{"className":3333,"style":852},[615,616]," liege in der Mitte des Intervalls. Im zweiten Beispiel ist ",[572,3336,3338,3358],{"className":3337},[575],[572,3339,3341],{"className":3340},[579],[581,3342,3343],{"xmlns":583},[585,3344,3345,3355],{},[588,3346,3347,3349,3351],{},[591,3348,835],{},[662,3350,879],{},[2835,3352,3353],{},[1053,3354,2086],{},[595,3356,3357],{"encoding":597},"\\xi = \\sqrt{3}",[572,3359,3361,3379],{"className":3360,"ariaHidden":602},[601],[572,3362,3364,3367,3370,3373,3376],{"className":3363},[606],[572,3365],{"className":3366,"style":848},[610],[572,3368,835],{"className":3369,"style":852},[615,616],[572,3371],{"className":3372,"style":707},[706],[572,3374,879],{"className":3375},[711],[572,3377],{"className":3378,"style":707},[706],[572,3380,3382,3385],{"className":3381},[606],[572,3383],{"className":3384,"style":2875},[610],[572,3386,3388],{"className":3387},[615,2879],[572,3389,3391,3424],{"className":3390},[1082,2178],[572,3392,3394,3421],{"className":3393},[1086],[572,3395,3397,3409],{"className":3396,"style":2889},[1090],[572,3398,3400,3403],{"className":3399,"style":2894},[2893],[572,3401],{"className":3402,"style":2192},[1098],[572,3404,3406],{"className":3405,"style":2901},[615],[572,3407,2086],{"className":3408},[615],[572,3410,3411,3414],{"style":2907},[572,3412],{"className":3413,"style":2192},[1098],[572,3415,3417],{"className":3416,"style":2915},[2914],[2917,3418,3419],{"xmlns":2919,"width":2920,"height":2921,"viewBox":2922,"preserveAspectRatio":2923},[2925,3420],{"d":2927},[572,3422,2238],{"className":3423},[2237],[572,3425,3427],{"className":3426},[1086],[572,3428,3430],{"className":3429,"style":2937},[1090],[572,3431],{},", nicht ",[572,3434,3436,3451],{"className":3435},[575],[572,3437,3439],{"className":3438},[579],[581,3440,3441],{"xmlns":583},[585,3442,3443,3448],{},[588,3444,3445],{},[1053,3446,3447],{},"1,5",[595,3449,3450],{"encoding":597},"1{,}5",[572,3452,3454],{"className":3453,"ariaHidden":602},[601],[572,3455,3457,3460,3463,3469],{"className":3456},[606],[572,3458],{"className":3459,"style":2955},[610],[572,3461,1770],{"className":3462},[615],[572,3464,3466],{"className":3465},[615],[572,3467,966],{"className":3468},[1010],[572,3470,3472],{"className":3471},[615],"5",[1149,3474,3475,3476,3504,3505,2064,3545,3604,3605,3633,3634,3695],{},"Erwarten, dass ",[572,3477,3479,3492],{"className":3478},[575],[572,3480,3482],{"className":3481},[579],[581,3483,3484],{"xmlns":583},[585,3485,3486,3490],{},[588,3487,3488],{},[591,3489,835],{},[595,3491,838],{"encoding":597},[572,3493,3495],{"className":3494,"ariaHidden":602},[601],[572,3496,3498,3501],{"className":3497},[606],[572,3499],{"className":3500,"style":848},[610],[572,3502,835],{"className":3503,"style":852},[615,616]," eindeutig ist. Bei ",[572,3506,3508,3526],{"className":3507},[575],[572,3509,3511],{"className":3510},[579],[581,3512,3513],{"xmlns":583},[585,3514,3515,3523],{},[588,3516,3517,3519,3521],{},[591,3518,1837],{},[662,3520,1760],{},[591,3522,1763],{},[595,3524,3525],{"encoding":597},"\\sin x",[572,3527,3529],{"className":3528,"ariaHidden":602},[601],[572,3530,3532,3536,3539,3542],{"className":3531},[606],[572,3533],{"className":3534,"style":3535},[610],"height:0.6679em;",[572,3537,1837],{"className":3538},[1792],[572,3540],{"className":3541,"style":1014},[706],[572,3543,1763],{"className":3544},[615,616],[572,3546,3548,3573],{"className":3547},[575],[572,3549,3551],{"className":3550},[579],[581,3552,3553],{"xmlns":583},[585,3554,3555,3570],{},[588,3556,3557,3559,3561,3563,3565,3568],{},[662,3558,2079],{"stretchy":664},[1053,3560,1055],{},[662,3562,966],{"separator":602},[1053,3564,2151],{},[591,3566,3567],{},"π",[662,3569,2089],{"stretchy":664},[595,3571,3572],{"encoding":597},"[0, 4\\pi]",[572,3574,3576],{"className":3575,"ariaHidden":602},[601],[572,3577,3579,3582,3585,3588,3591,3594,3597,3601],{"className":3578},[606],[572,3580],{"className":3581,"style":695},[610],[572,3583,2079],{"className":3584},[699],[572,3586,1055],{"className":3587},[615],[572,3589,966],{"className":3590},[1010],[572,3592],{"className":3593,"style":1014},[706],[572,3595,2151],{"className":3596},[615],[572,3598,3567],{"className":3599,"style":3600},[615,616],"margin-right:0.0359em;",[572,3602,2089],{"className":3603},[734]," ist die Sekantensteigung ",[572,3606,3608,3621],{"className":3607},[575],[572,3609,3611],{"className":3610},[579],[581,3612,3613],{"xmlns":583},[585,3614,3615,3619],{},[588,3616,3617],{},[1053,3618,1055],{},[595,3620,1055],{"encoding":597},[572,3622,3624],{"className":3623,"ariaHidden":602},[601],[572,3625,3627,3630],{"className":3626},[606],[572,3628],{"className":3629,"style":1137},[610],[572,3631,1055],{"className":3632},[615],", und ",[572,3635,3637,3659],{"className":3636},[575],[572,3638,3640],{"className":3639},[579],[581,3641,3642],{"xmlns":583},[585,3643,3644,3656],{},[588,3645,3646,3648,3650,3652,3654],{},[591,3647,1757],{},[662,3649,1760],{},[591,3651,835],{},[662,3653,879],{},[1053,3655,1055],{},[595,3657,3658],{"encoding":597},"\\cos \\xi = 0",[572,3660,3662,3686],{"className":3661,"ariaHidden":602},[601],[572,3663,3665,3668,3671,3674,3677,3680,3683],{"className":3664},[606],[572,3666],{"className":3667,"style":848},[610],[572,3669,1757],{"className":3670},[1792],[572,3672],{"className":3673,"style":1014},[706],[572,3675,835],{"className":3676,"style":852},[615,616],[572,3678],{"className":3679,"style":707},[706],[572,3681,879],{"className":3682},[711],[572,3684],{"className":3685,"style":707},[706],[572,3687,3689,3692],{"className":3688},[606],[572,3690],{"className":3691,"style":1137},[610],[572,3693,1055],{"className":3694},[615]," hat dort vier Lösungen.",{"title":3697,"searchDepth":3698,"depth":3698,"links":3699},"",2,[3700,3701,3702],{"id":561,"depth":3698,"text":562},{"id":1962,"depth":3698,"text":1963},{"id":2972,"depth":3698,"text":2973},[3704,3706,3708,3710,3712,3715,3717,3719],{"lhs":3705,"rhs":2151},"(3^2 - 1^2)\u002F(3 - 1)",{"lhs":3707,"rhs":2151},"2*2",{"lhs":3709,"rhs":2140},"(3^3 - 0^3)\u002F(3 - 0)",{"lhs":3711,"rhs":2140},"3*sqrt(3)^2",{"lhs":3713,"rhs":3714},"round(sqrt(3), 3)","1.732",{"lhs":3716,"rhs":1055},"(abs(1) - abs(-1))\u002F(1 - (-1))",{"lhs":3718,"rhs":1055},"round((sin(4*pi) - sin(0))\u002F(4*pi), 9)",{"lhs":3720,"rhs":1055},"round(cos(7*pi\u002F2), 9)","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 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