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0",[580,1094,1096,1152],{"className":1095,"ariaHidden":637},[636],[580,1097,1099,1102,1134,1137,1140,1143,1146,1149],{"className":1098},[641],[580,1100],{"className":1101,"style":646},[645],[580,1103,1105,1108],{"className":1104},[650],[580,1106,604],{"className":1107,"style":655},[650,654],[580,1109,1111],{"className":1110},[659],[580,1112,1114],{"className":1113},[663],[580,1115,1117],{"className":1116},[667],[580,1118,1120],{"className":1119,"style":672},[671],[580,1121,1122,1125],{"style":675},[580,1123],{"className":1124,"style":680},[679],[580,1126,1128],{"className":1127},[684,685,686,687],[580,1129,1131],{"className":1130},[650,687],[580,1132,610],{"className":1133},[650,687],[580,1135,614],{"className":1136},[697],[580,1138,617],{"className":1139},[650,654],[580,1141,620],{"className":1142},[704],[580,1144],{"className":1145,"style":709},[708],[580,1147,1087],{"className":1148},[713],[580,1150],{"className":1151,"style":709},[708],[580,1153,1155,1158],{"className":1154},[641],[580,1156],{"className":1157,"style":723},[645],[580,1159,627],{"className":1160},[650],[580,1162,1164,1181],{"className":1163},[583],[580,1165,1167],{"className":1166},[587],[589,1168,1169],{"xmlns":591},[593,1170,1171,1179],{},[596,1172,1173,1175,1177],{},[602,1174,617],{},[606,1176,744],{},[602,1178,747],{},[629,1180,750],{"encoding":631},[580,1182,1184,1202],{"className":1183,"ariaHidden":637},[636],[580,1185,1187,1190,1193,1196,1199],{"className":1186},[641],[580,1188],{"className":1189,"style":760},[645],[580,1191,617],{"className":1192},[650,654],[580,1194],{"className":1195,"style":709},[708],[580,1197,744],{"className":1198},[713],[580,1200],{"className":1201,"style":709},[708],[580,1203,1205,1208],{"className":1204},[641],[580,1206],{"className":1207,"style":779},[645],[580,1209,747],{"className":1210,"style":783},[650,654],[580,1212,1214,1227],{"className":1213},[583],[580,1215,1217],{"className":1216},[587],[589,1218,1219],{"xmlns":591},[593,1220,1221,1225],{},[596,1222,1223],{},[602,1224,604],{},[629,1226,604],{"encoding":631},[580,1228,1230],{"className":1229,"ariaHidden":637},[636],[580,1231,1233,1236],{"className":1232},[641],[580,1234],{"className":1235,"style":810},[645],[580,1237,604],{"className":1238,"style":655},[650,654],[580,1240,1242,1255],{"className":1241},[583],[580,1243,1245],{"className":1244},[587],[589,1246,1247],{"xmlns":591},[593,1248,1249,1253],{},[596,1250,1251],{},[602,1252,747],{},[629,1254,747],{"encoding":631},[580,1256,1258],{"className":1257,"ariaHidden":637},[636],[580,1259,1261,1264],{"className":1260},[641],[580,1262],{"className":1263,"style":779},[645],[580,1265,747],{"className":1266,"style":783},[650,654]," monoton wachsend, und umgekehrt. Ebenso für ",[580,1269,1271,1300],{"className":1270},[583],[580,1272,1274],{"className":1273},[587],[589,1275,1276],{"xmlns":591},[593,1277,1278,1297],{},[596,1279,1280,1286,1288,1290,1292,1295],{},[599,1281,1282,1284],{},[602,1283,604],{},[606,1285,610],{"mathvariant":608,"lspace":609,"rspace":609},[606,1287,614],{"stretchy":613},[602,1289,617],{},[606,1291,620],{"stretchy":613},[606,1293,1294],{},"≤",[625,1296,627],{},[629,1298,1299],{"encoding":631},"f'(x) \\leq 0",[580,1301,1303,1359],{"className":1302,"ariaHidden":637},[636],[580,1304,1306,1309,1341,1344,1347,1350,1353,1356],{"className":1305},[641],[580,1307],{"className":1308,"style":646},[645],[580,1310,1312,1315],{"className":1311},[650],[580,1313,604],{"className":1314,"style":655},[650,654],[580,1316,1318],{"className":1317},[659],[580,1319,1321],{"className":1320},[663],[580,1322,1324],{"className":1323},[667],[580,1325,1327],{"className":1326,"style":672},[671],[580,1328,1329,1332],{"style":675},[580,1330],{"className":1331,"style":680},[679],[580,1333,1335],{"className":1334},[684,685,686,687],[580,1336,1338],{"className":1337},[650,687],[580,1339,610],{"className":1340},[650,687],[580,1342,614],{"className":1343},[697],[580,1345,617],{"className":1346},[650,654],[580,1348,620],{"className":1349},[704],[580,1351],{"className":1352,"style":709},[708],[580,1354,1294],{"className":1355},[713],[580,1357],{"className":1358,"style":709},[708],[580,1360,1362,1365],{"className":1361},[641],[580,1363],{"className":1364,"style":723},[645],[580,1366,627],{"className":1367},[650]," und monoton fallend.",[565,1370,1371,1372,1375,1376,1439,1440,847],{},"Die strenge Version ist nur ",[569,1373,1374],{},"hinreichend",": Einzelne Nullstellen von ",[580,1377,1379,1397],{"className":1378},[583],[580,1380,1382],{"className":1381},[587],[589,1383,1384],{"xmlns":591},[593,1385,1386,1394],{},[596,1387,1388],{},[599,1389,1390,1392],{},[602,1391,604],{},[606,1393,610],{"mathvariant":608,"lspace":609,"rspace":609},[629,1395,1396],{"encoding":631},"f'",[580,1398,1400],{"className":1399,"ariaHidden":637},[636],[580,1401,1403,1407],{"className":1402},[641],[580,1404],{"className":1405,"style":1406},[645],"height:0.9463em;vertical-align:-0.1944em;",[580,1408,1410,1413],{"className":1409},[650],[580,1411,604],{"className":1412,"style":655},[650,654],[580,1414,1416],{"className":1415},[659],[580,1417,1419],{"className":1418},[663],[580,1420,1422],{"className":1421},[667],[580,1423,1425],{"className":1424,"style":672},[671],[580,1426,1427,1430],{"style":675},[580,1428],{"className":1429,"style":680},[679],[580,1431,1433],{"className":1432},[684,685,686,687],[580,1434,1436],{"className":1435},[650,687],[580,1437,610],{"className":1438},[650,687]," stören die strenge Monotonie nicht, wie bei ",[580,1441,1443,1473],{"className":1442},[583],[580,1444,1446],{"className":1445},[587],[589,1447,1448],{"xmlns":591},[593,1449,1450,1470],{},[596,1451,1452,1454,1456,1458,1460,1463],{},[602,1453,604],{},[606,1455,614],{"stretchy":613},[602,1457,617],{},[606,1459,620],{"stretchy":613},[606,1461,1462],{},"=",[599,1464,1465,1467],{},[602,1466,617],{},[625,1468,1469],{},"3",[629,1471,1472],{"encoding":631},"f(x) = x^3",[580,1474,1476,1504],{"className":1475,"ariaHidden":637},[636],[580,1477,1479,1483,1486,1489,1492,1495,1498,1501],{"className":1478},[641],[580,1480],{"className":1481,"style":1482},[645],"height:1em;vertical-align:-0.25em;",[580,1484,604],{"className":1485,"style":655},[650,654],[580,1487,614],{"className":1488},[697],[580,1490,617],{"className":1491},[650,654],[580,1493,620],{"className":1494},[704],[580,1496],{"className":1497,"style":709},[708],[580,1499,1462],{"className":1500},[713],[580,1502],{"className":1503,"style":709},[708],[580,1505,1507,1511],{"className":1506},[641],[580,1508],{"className":1509,"style":1510},[645],"height:0.8141em;",[580,1512,1514,1517],{"className":1513},[650],[580,1515,617],{"className":1516},[650,654],[580,1518,1520],{"className":1519},[659],[580,1521,1523],{"className":1522},[663],[580,1524,1526],{"className":1525},[667],[580,1527,1529],{"className":1528,"style":1510},[671],[580,1530,1531,1534],{"style":675},[580,1532],{"className":1533,"style":680},[679],[580,1535,1537],{"className":1536},[684,685,686,687],[580,1538,1469],{"className":1539},[650,687],[565,1541,1542,1543,1612],{},"Das Kriterium gilt nur auf Intervallen. Auf einer Menge mit Lücke, z.B. ",[580,1544,1546,1573],{"className":1545},[583],[580,1547,1549],{"className":1548},[587],[589,1550,1551],{"xmlns":591},[593,1552,1553,1570],{},[596,1554,1555,1559,1562,1565,1567],{},[602,1556,1558],{"mathvariant":1557},"double-struck","R",[606,1560,1561],{},"∖",[606,1563,1564],{"stretchy":613},"{",[625,1566,627],{},[606,1568,1569],{"stretchy":613},"}",[629,1571,1572],{"encoding":631},"\\mathbb{R} \\setminus \\{0\\}",[580,1574,1576,1597],{"className":1575,"ariaHidden":637},[636],[580,1577,1579,1582,1586,1590,1594],{"className":1578},[641],[580,1580],{"className":1581,"style":1482},[645],[580,1583,1558],{"className":1584},[650,1585],"mathbb",[580,1587],{"className":1588,"style":1589},[708],"margin-right:0.2222em;",[580,1591,1561],{"className":1592},[1593],"mbin",[580,1595],{"className":1596,"style":1589},[708],[580,1598,1600,1603,1606,1609],{"className":1599},[641],[580,1601],{"className":1602,"style":1482},[645],[580,1604,1564],{"className":1605},[697],[580,1607,627],{"className":1608},[650],[580,1610,1569],{"className":1611},[704],", kann man daraus nichts schließen.",[565,1614,1615,1618,1619,1680,1681,1742],{},[569,1616,1617],{},"Vorgehen:"," Nullstellen von ",[580,1620,1622,1639],{"className":1621},[583],[580,1623,1625],{"className":1624},[587],[589,1626,1627],{"xmlns":591},[593,1628,1629,1637],{},[596,1630,1631],{},[599,1632,1633,1635],{},[602,1634,604],{},[606,1636,610],{"mathvariant":608,"lspace":609,"rspace":609},[629,1638,1396],{"encoding":631},[580,1640,1642],{"className":1641,"ariaHidden":637},[636],[580,1643,1645,1648],{"className":1644},[641],[580,1646],{"className":1647,"style":1406},[645],[580,1649,1651,1654],{"className":1650},[650],[580,1652,604],{"className":1653,"style":655},[650,654],[580,1655,1657],{"className":1656},[659],[580,1658,1660],{"className":1659},[663],[580,1661,1663],{"className":1662},[667],[580,1664,1666],{"className":1665,"style":672},[671],[580,1667,1668,1671],{"style":675},[580,1669],{"className":1670,"style":680},[679],[580,1672,1674],{"className":1673},[684,685,686,687],[580,1675,1677],{"className":1676},[650,687],[580,1678,610],{"className":1679},[650,687]," (und Definitionslücken) bestimmen, die Zahlengerade daran in Intervalle teilen und in jedem Intervall das Vorzeichen von ",[580,1682,1684,1701],{"className":1683},[583],[580,1685,1687],{"className":1686},[587],[589,1688,1689],{"xmlns":591},[593,1690,1691,1699],{},[596,1692,1693],{},[599,1694,1695,1697],{},[602,1696,604],{},[606,1698,610],{"mathvariant":608,"lspace":609,"rspace":609},[629,1700,1396],{"encoding":631},[580,1702,1704],{"className":1703,"ariaHidden":637},[636],[580,1705,1707,1710],{"className":1706},[641],[580,1708],{"className":1709,"style":1406},[645],[580,1711,1713,1716],{"className":1712},[650],[580,1714,604],{"className":1715,"style":655},[650,654],[580,1717,1719],{"className":1718},[659],[580,1720,1722],{"className":1721},[663],[580,1723,1725],{"className":1724},[667],[580,1726,1728],{"className":1727,"style":672},[671],[580,1729,1730,1733],{"style":675},[580,1731],{"className":1732,"style":680},[679],[580,1734,1736],{"className":1735},[684,685,686,687],[580,1737,1739],{"className":1738},[650,687],[580,1740,610],{"className":1741},[650,687]," mit einem Testwert ermitteln.",[560,1744,1746],{"id":1745},"beispiele","Beispiele",[565,1748,1749,1874,1875,2130,2131,2166,2167,2195,2196,2226],{},[580,1750,1752,1787],{"className":1751},[583],[580,1753,1755],{"className":1754},[587],[589,1756,1757],{"xmlns":591},[593,1758,1759,1784],{},[596,1760,1761,1763,1765,1767,1769,1771,1777,1780,1782],{},[602,1762,604],{},[606,1764,614],{"stretchy":613},[602,1766,617],{},[606,1768,620],{"stretchy":613},[606,1770,1462],{},[599,1772,1773,1775],{},[602,1774,617],{},[625,1776,1469],{},[606,1778,1779],{},"−",[625,1781,1469],{},[602,1783,617],{},[629,1785,1786],{"encoding":631},"f(x) = x^3 - 3x",[580,1788,1790,1817,1862],{"className":1789,"ariaHidden":637},[636],[580,1791,1793,1796,1799,1802,1805,1808,1811,1814],{"className":1792},[641],[580,1794],{"className":1795,"style":1482},[645],[580,1797,604],{"className":1798,"style":655},[650,654],[580,1800,614],{"className":1801},[697],[580,1803,617],{"className":1804},[650,654],[580,1806,620],{"className":1807},[704],[580,1809],{"className":1810,"style":709},[708],[580,1812,1462],{"className":1813},[713],[580,1815],{"className":1816,"style":709},[708],[580,1818,1820,1824,1853,1856,1859],{"className":1819},[641],[580,1821],{"className":1822,"style":1823},[645],"height:0.8974em;vertical-align:-0.0833em;",[580,1825,1827,1830],{"className":1826},[650],[580,1828,617],{"className":1829},[650,654],[580,1831,1833],{"className":1832},[659],[580,1834,1836],{"className":1835},[663],[580,1837,1839],{"className":1838},[667],[580,1840,1842],{"className":1841,"style":1510},[671],[580,1843,1844,1847],{"style":675},[580,1845],{"className":1846,"style":680},[679],[580,1848,1850],{"className":1849},[684,685,686,687],[580,1851,1469],{"className":1852},[650,687],[580,1854],{"className":1855,"style":1589},[708],[580,1857,1779],{"className":1858},[1593],[580,1860],{"className":1861,"style":1589},[708],[580,1863,1865,1868,1871],{"className":1864},[641],[580,1866],{"className":1867,"style":723},[645],[580,1869,1469],{"className":1870},[650],[580,1872,617],{"className":1873},[650,654]," mit ",[580,1876,1878,1943],{"className":1877},[583],[580,1879,1881],{"className":1880},[587],[589,1882,1883],{"xmlns":591},[593,1884,1885,1940],{},[596,1886,1887,1893,1895,1897,1899,1901,1903,1910,1912,1914,1916,1918,1920,1922,1924,1927,1929,1931,1933,1936,1938],{},[599,1888,1889,1891],{},[602,1890,604],{},[606,1892,610],{"mathvariant":608,"lspace":609,"rspace":609},[606,1894,614],{"stretchy":613},[602,1896,617],{},[606,1898,620],{"stretchy":613},[606,1900,1462],{},[625,1902,1469],{},[599,1904,1905,1907],{},[602,1906,617],{},[625,1908,1909],{},"2",[606,1911,1779],{},[625,1913,1469],{},[606,1915,1462],{},[625,1917,1469],{},[606,1919,614],{"stretchy":613},[602,1921,617],{},[606,1923,1779],{},[625,1925,1926],{},"1",[606,1928,620],{"stretchy":613},[606,1930,614],{"stretchy":613},[602,1932,617],{},[606,1934,1935],{},"+",[625,1937,1926],{},[606,1939,620],{"stretchy":613},[629,1941,1942],{"encoding":631},"f'(x) = 3x^2 - 3 = 3(x - 1)(x + 1)",[580,1944,1946,2002,2049,2067,2091,2118],{"className":1945,"ariaHidden":637},[636],[580,1947,1949,1952,1984,1987,1990,1993,1996,1999],{"className":1948},[641],[580,1950],{"className":1951,"style":646},[645],[580,1953,1955,1958],{"className":1954},[650],[580,1956,604],{"className":1957,"style":655},[650,654],[580,1959,1961],{"className":1960},[659],[580,1962,1964],{"className":1963},[663],[580,1965,1967],{"className":1966},[667],[580,1968,1970],{"className":1969,"style":672},[671],[580,1971,1972,1975],{"style":675},[580,1973],{"className":1974,"style":680},[679],[580,1976,1978],{"className":1977},[684,685,686,687],[580,1979,1981],{"className":1980},[650,687],[580,1982,610],{"className":1983},[650,687],[580,1985,614],{"className":1986},[697],[580,1988,617],{"className":1989},[650,654],[580,1991,620],{"className":1992},[704],[580,1994],{"className":1995,"style":709},[708],[580,1997,1462],{"className":1998},[713],[580,2000],{"className":2001,"style":709},[708],[580,2003,2005,2008,2011,2040,2043,2046],{"className":2004},[641],[580,2006],{"className":2007,"style":1823},[645],[580,2009,1469],{"className":2010},[650],[580,2012,2014,2017],{"className":2013},[650],[580,2015,617],{"className":2016},[650,654],[580,2018,2020],{"className":2019},[659],[580,2021,2023],{"className":2022},[663],[580,2024,2026],{"className":2025},[667],[580,2027,2029],{"className":2028,"style":1510},[671],[580,2030,2031,2034],{"style":675},[580,2032],{"className":2033,"style":680},[679],[580,2035,2037],{"className":2036},[684,685,686,687],[580,2038,1909],{"className":2039},[650,687],[580,2041],{"className":2042,"style":1589},[708],[580,2044,1779],{"className":2045},[1593],[580,2047],{"className":2048,"style":1589},[708],[580,2050,2052,2055,2058,2061,2064],{"className":2051},[641],[580,2053],{"className":2054,"style":723},[645],[580,2056,1469],{"className":2057},[650],[580,2059],{"className":2060,"style":709},[708],[580,2062,1462],{"className":2063},[713],[580,2065],{"className":2066,"style":709},[708],[580,2068,2070,2073,2076,2079,2082,2085,2088],{"className":2069},[641],[580,2071],{"className":2072,"style":1482},[645],[580,2074,1469],{"className":2075},[650],[580,2077,614],{"className":2078},[697],[580,2080,617],{"className":2081},[650,654],[580,2083],{"className":2084,"style":1589},[708],[580,2086,1779],{"className":2087},[1593],[580,2089],{"className":2090,"style":1589},[708],[580,2092,2094,2097,2100,2103,2106,2109,2112,2115],{"className":2093},[641],[580,2095],{"className":2096,"style":1482},[645],[580,2098,1926],{"className":2099},[650],[580,2101,620],{"className":2102},[704],[580,2104,614],{"className":2105},[697],[580,2107,617],{"className":2108},[650,654],[580,2110],{"className":2111,"style":1589},[708],[580,2113,1935],{"className":2114},[1593],[580,2116],{"className":2117,"style":1589},[708],[580,2119,2121,2124,2127],{"className":2120},[641],[580,2122],{"className":2123,"style":1482},[645],[580,2125,1926],{"className":2126},[650],[580,2128,620],{"className":2129},[704],". Die Nullstellen ",[580,2132,2134,2150],{"className":2133},[583],[580,2135,2137],{"className":2136},[587],[589,2138,2139],{"xmlns":591},[593,2140,2141,2147],{},[596,2142,2143,2145],{},[606,2144,1779],{},[625,2146,1926],{},[629,2148,2149],{"encoding":631},"-1",[580,2151,2153],{"className":2152,"ariaHidden":637},[636],[580,2154,2156,2160,2163],{"className":2155},[641],[580,2157],{"className":2158,"style":2159},[645],"height:0.7278em;vertical-align:-0.0833em;",[580,2161,1779],{"className":2162},[650],[580,2164,1926],{"className":2165},[650]," und ",[580,2168,2170,2183],{"className":2169},[583],[580,2171,2173],{"className":2172},[587],[589,2174,2175],{"xmlns":591},[593,2176,2177,2181],{},[596,2178,2179],{},[625,2180,1926],{},[629,2182,1926],{"encoding":631},[580,2184,2186],{"className":2185,"ariaHidden":637},[636],[580,2187,2189,2192],{"className":2188},[641],[580,2190],{"className":2191,"style":723},[645],[580,2193,1926],{"className":2194},[650]," teilen ",[580,2197,2199,2213],{"className":2198},[583],[580,2200,2202],{"className":2201},[587],[589,2203,2204],{"xmlns":591},[593,2205,2206,2210],{},[596,2207,2208],{},[602,2209,1558],{"mathvariant":1557},[629,2211,2212],{"encoding":631},"\\mathbb{R}",[580,2214,2216],{"className":2215,"ariaHidden":637},[636],[580,2217,2219,2223],{"className":2218},[641],[580,2220],{"className":2221,"style":2222},[645],"height:0.6889em;",[580,2224,1558],{"className":2225},[650,1585]," in drei Intervalle. Testwerte:",[574,2228,2229,2455,2670],{},[577,2230,2231,784,2359,2387,2388,847],{},[580,2232,2234,2269],{"className":2233},[583],[580,2235,2237],{"className":2236},[587],[589,2238,2239],{"xmlns":591},[593,2240,2241,2266],{},[596,2242,2243,2249,2251,2253,2255,2257,2259,2262,2264],{},[599,2244,2245,2247],{},[602,2246,604],{},[606,2248,610],{"mathvariant":608,"lspace":609,"rspace":609},[606,2250,614],{"stretchy":613},[606,2252,1779],{},[625,2254,1909],{},[606,2256,620],{"stretchy":613},[606,2258,1462],{},[625,2260,2261],{},"9",[606,2263,623],{},[625,2265,627],{},[629,2267,2268],{"encoding":631},"f'(-2) = 9 > 0",[580,2270,2272,2331,2350],{"className":2271,"ariaHidden":637},[636],[580,2273,2275,2278,2310,2313,2316,2319,2322,2325,2328],{"className":2274},[641],[580,2276],{"className":2277,"style":646},[645],[580,2279,2281,2284],{"className":2280},[650],[580,2282,604],{"className":2283,"style":655},[650,654],[580,2285,2287],{"className":2286},[659],[580,2288,2290],{"className":2289},[663],[580,2291,2293],{"className":2292},[667],[580,2294,2296],{"className":2295,"style":672},[671],[580,2297,2298,2301],{"style":675},[580,2299],{"className":2300,"style":680},[679],[580,2302,2304],{"className":2303},[684,685,686,687],[580,2305,2307],{"className":2306},[650,687],[580,2308,610],{"className":2309},[650,687],[580,2311,614],{"className":2312},[697],[580,2314,1779],{"className":2315},[650],[580,2317,1909],{"className":2318},[650],[580,2320,620],{"className":2321},[704],[580,2323],{"className":2324,"style":709},[708],[580,2326,1462],{"className":2327},[713],[580,2329],{"className":2330,"style":709},[708],[580,2332,2334,2338,2341,2344,2347],{"className":2333},[641],[580,2335],{"className":2336,"style":2337},[645],"height:0.6835em;vertical-align:-0.0391em;",[580,2339,2261],{"className":2340},[650],[580,2342],{"className":2343,"style":709},[708],[580,2345,623],{"className":2346},[713],[580,2348],{"className":2349,"style":709},[708],[580,2351,2353,2356],{"className":2352},[641],[580,2354],{"className":2355,"style":723},[645],[580,2357,627],{"className":2358},[650],[580,2360,2362,2375],{"className":2361},[583],[580,2363,2365],{"className":2364},[587],[589,2366,2367],{"xmlns":591},[593,2368,2369,2373],{},[596,2370,2371],{},[602,2372,604],{},[629,2374,604],{"encoding":631},[580,2376,2378],{"className":2377,"ariaHidden":637},[636],[580,2379,2381,2384],{"className":2380},[641],[580,2382],{"className":2383,"style":810},[645],[580,2385,604],{"className":2386,"style":655},[650,654]," steigt streng auf ",[580,2389,2391,2420],{"className":2390},[583],[580,2392,2394],{"className":2393},[587],[589,2395,2396],{"xmlns":591},[593,2397,2398,2417],{},[596,2399,2400,2402,2404,2407,2410,2412,2414],{},[606,2401,614],{"stretchy":613},[606,2403,1779],{},[602,2405,2406],{"mathvariant":608},"∞",[606,2408,2409],{"separator":637},",",[606,2411,1779],{},[625,2413,1926],{},[606,2415,2416],{"stretchy":613},"]",[629,2418,2419],{"encoding":631},"(-\\infty, -1]",[580,2421,2423],{"className":2422,"ariaHidden":637},[636],[580,2424,2426,2429,2432,2435,2438,2442,2446,2449,2452],{"className":2425},[641],[580,2427],{"className":2428,"style":1482},[645],[580,2430,614],{"className":2431},[697],[580,2433,1779],{"className":2434},[650],[580,2436,2406],{"className":2437},[650],[580,2439,2409],{"className":2440},[2441],"mpunct",[580,2443],{"className":2444,"style":2445},[708],"margin-right:0.1667em;",[580,2447,1779],{"className":2448},[650],[580,2450,1926],{"className":2451},[650],[580,2453,2416],{"className":2454},[704],[577,2456,2457,784,2583,2611,2612,847],{},[580,2458,2460,2494],{"className":2459},[583],[580,2461,2463],{"className":2462},[587],[589,2464,2465],{"xmlns":591},[593,2466,2467,2491],{},[596,2468,2469,2475,2477,2479,2481,2483,2485,2487,2489],{},[599,2470,2471,2473],{},[602,2472,604],{},[606,2474,610],{"mathvariant":608,"lspace":609,"rspace":609},[606,2476,614],{"stretchy":613},[625,2478,627],{},[606,2480,620],{"stretchy":613},[606,2482,1462],{},[606,2484,1779],{},[625,2486,1469],{},[606,2488,876],{},[625,2490,627],{},[629,2492,2493],{"encoding":631},"f'(0) = -3 \u003C 0",[580,2495,2497,2553,2574],{"className":2496,"ariaHidden":637},[636],[580,2498,2500,2503,2535,2538,2541,2544,2547,2550],{"className":2499},[641],[580,2501],{"className":2502,"style":646},[645],[580,2504,2506,2509],{"className":2505},[650],[580,2507,604],{"className":2508,"style":655},[650,654],[580,2510,2512],{"className":2511},[659],[580,2513,2515],{"className":2514},[663],[580,2516,2518],{"className":2517},[667],[580,2519,2521],{"className":2520,"style":672},[671],[580,2522,2523,2526],{"style":675},[580,2524],{"className":2525,"style":680},[679],[580,2527,2529],{"className":2528},[684,685,686,687],[580,2530,2532],{"className":2531},[650,687],[580,2533,610],{"className":2534},[650,687],[580,2536,614],{"className":2537},[697],[580,2539,627],{"className":2540},[650],[580,2542,620],{"className":2543},[704],[580,2545],{"className":2546,"style":709},[708],[580,2548,1462],{"className":2549},[713],[580,2551],{"className":2552,"style":709},[708],[580,2554,2556,2559,2562,2565,2568,2571],{"className":2555},[641],[580,2557],{"className":2558,"style":2159},[645],[580,2560,1779],{"className":2561},[650],[580,2563,1469],{"className":2564},[650],[580,2566],{"className":2567,"style":709},[708],[580,2569,876],{"className":2570},[713],[580,2572],{"className":2573,"style":709},[708],[580,2575,2577,2580],{"className":2576},[641],[580,2578],{"className":2579,"style":723},[645],[580,2581,627],{"className":2582},[650],[580,2584,2586,2599],{"className":2585},[583],[580,2587,2589],{"className":2588},[587],[589,2590,2591],{"xmlns":591},[593,2592,2593,2597],{},[596,2594,2595],{},[602,2596,604],{},[629,2598,604],{"encoding":631},[580,2600,2602],{"className":2601,"ariaHidden":637},[636],[580,2603,2605,2608],{"className":2604},[641],[580,2606],{"className":2607,"style":810},[645],[580,2609,604],{"className":2610,"style":655},[650,654]," fällt streng auf ",[580,2613,2615,2640],{"className":2614},[583],[580,2616,2618],{"className":2617},[587],[589,2619,2620],{"xmlns":591},[593,2621,2622,2637],{},[596,2623,2624,2627,2629,2631,2633,2635],{},[606,2625,2626],{"stretchy":613},"[",[606,2628,1779],{},[625,2630,1926],{},[606,2632,2409],{"separator":637},[625,2634,1926],{},[606,2636,2416],{"stretchy":613},[629,2638,2639],{"encoding":631},"[-1, 1]",[580,2641,2643],{"className":2642,"ariaHidden":637},[636],[580,2644,2646,2649,2652,2655,2658,2661,2664,2667],{"className":2645},[641],[580,2647],{"className":2648,"style":1482},[645],[580,2650,2626],{"className":2651},[697],[580,2653,1779],{"className":2654},[650],[580,2656,1926],{"className":2657},[650],[580,2659,2409],{"className":2660},[2441],[580,2662],{"className":2663,"style":2445},[708],[580,2665,1926],{"className":2666},[650],[580,2668,2416],{"className":2669},[704],[577,2671,2672,784,2793,2387,2821,847],{},[580,2673,2675,2707],{"className":2674},[583],[580,2676,2678],{"className":2677},[587],[589,2679,2680],{"xmlns":591},[593,2681,2682,2704],{},[596,2683,2684,2690,2692,2694,2696,2698,2700,2702],{},[599,2685,2686,2688],{},[602,2687,604],{},[606,2689,610],{"mathvariant":608,"lspace":609,"rspace":609},[606,2691,614],{"stretchy":613},[625,2693,1909],{},[606,2695,620],{"stretchy":613},[606,2697,1462],{},[625,2699,2261],{},[606,2701,623],{},[625,2703,627],{},[629,2705,2706],{"encoding":631},"f'(2) = 9 > 0",[580,2708,2710,2766,2784],{"className":2709,"ariaHidden":637},[636],[580,2711,2713,2716,2748,2751,2754,2757,2760,2763],{"className":2712},[641],[580,2714],{"className":2715,"style":646},[645],[580,2717,2719,2722],{"className":2718},[650],[580,2720,604],{"className":2721,"style":655},[650,654],[580,2723,2725],{"className":2724},[659],[580,2726,2728],{"className":2727},[663],[580,2729,2731],{"className":2730},[667],[580,2732,2734],{"className":2733,"style":672},[671],[580,2735,2736,2739],{"style":675},[580,2737],{"className":2738,"style":680},[679],[580,2740,2742],{"className":2741},[684,685,686,687],[580,2743,2745],{"className":2744},[650,687],[580,2746,610],{"className":2747},[650,687],[580,2749,614],{"className":2750},[697],[580,2752,1909],{"className":2753},[650],[580,2755,620],{"className":2756},[704],[580,2758],{"className":2759,"style":709},[708],[580,2761,1462],{"className":2762},[713],[580,2764],{"className":2765,"style":709},[708],[580,2767,2769,2772,2775,2778,2781],{"className":2768},[641],[580,2770],{"className":2771,"style":2337},[645],[580,2773,2261],{"className":2774},[650],[580,2776],{"className":2777,"style":709},[708],[580,2779,623],{"className":2780},[713],[580,2782],{"className":2783,"style":709},[708],[580,2785,2787,2790],{"className":2786},[641],[580,2788],{"className":2789,"style":723},[645],[580,2791,627],{"className":2792},[650],[580,2794,2796,2809],{"className":2795},[583],[580,2797,2799],{"className":2798},[587],[589,2800,2801],{"xmlns":591},[593,2802,2803,2807],{},[596,2804,2805],{},[602,2806,604],{},[629,2808,604],{"encoding":631},[580,2810,2812],{"className":2811,"ariaHidden":637},[636],[580,2813,2815,2818],{"className":2814},[641],[580,2816],{"className":2817,"style":810},[645],[580,2819,604],{"className":2820,"style":655},[650,654],[580,2822,2824,2846],{"className":2823},[583],[580,2825,2827],{"className":2826},[587],[589,2828,2829],{"xmlns":591},[593,2830,2831,2843],{},[596,2832,2833,2835,2837,2839,2841],{},[606,2834,2626],{"stretchy":613},[625,2836,1926],{},[606,2838,2409],{"separator":637},[602,2840,2406],{"mathvariant":608},[606,2842,620],{"stretchy":613},[629,2844,2845],{"encoding":631},"[1, \\infty)",[580,2847,2849],{"className":2848,"ariaHidden":637},[636],[580,2850,2852,2855,2858,2861,2864,2867,2870],{"className":2851},[641],[580,2853],{"className":2854,"style":1482},[645],[580,2856,2626],{"className":2857},[697],[580,2859,1926],{"className":2860},[650],[580,2862,2409],{"className":2863},[2441],[580,2865],{"className":2866,"style":2445},[708],[580,2868,2406],{"className":2869},[650],[580,2871,620],{"className":2872},[704],[565,2874,2875,2876,2947,2948,3019,3020,3048],{},"Die Funktion fällt also von ",[580,2877,2879,2905],{"className":2878},[583],[580,2880,2882],{"className":2881},[587],[589,2883,2884],{"xmlns":591},[593,2885,2886,2902],{},[596,2887,2888,2890,2892,2894,2896,2898,2900],{},[602,2889,604],{},[606,2891,614],{"stretchy":613},[606,2893,1779],{},[625,2895,1926],{},[606,2897,620],{"stretchy":613},[606,2899,1462],{},[625,2901,1909],{},[629,2903,2904],{"encoding":631},"f(-1) = 2",[580,2906,2908,2938],{"className":2907,"ariaHidden":637},[636],[580,2909,2911,2914,2917,2920,2923,2926,2929,2932,2935],{"className":2910},[641],[580,2912],{"className":2913,"style":1482},[645],[580,2915,604],{"className":2916,"style":655},[650,654],[580,2918,614],{"className":2919},[697],[580,2921,1779],{"className":2922},[650],[580,2924,1926],{"className":2925},[650],[580,2927,620],{"className":2928},[704],[580,2930],{"className":2931,"style":709},[708],[580,2933,1462],{"className":2934},[713],[580,2936],{"className":2937,"style":709},[708],[580,2939,2941,2944],{"className":2940},[641],[580,2942],{"className":2943,"style":723},[645],[580,2945,1909],{"className":2946},[650]," auf ",[580,2949,2951,2977],{"className":2950},[583],[580,2952,2954],{"className":2953},[587],[589,2955,2956],{"xmlns":591},[593,2957,2958,2974],{},[596,2959,2960,2962,2964,2966,2968,2970,2972],{},[602,2961,604],{},[606,2963,614],{"stretchy":613},[625,2965,1926],{},[606,2967,620],{"stretchy":613},[606,2969,1462],{},[606,2971,1779],{},[625,2973,1909],{},[629,2975,2976],{"encoding":631},"f(1) = -2",[580,2978,2980,3007],{"className":2979,"ariaHidden":637},[636],[580,2981,2983,2986,2989,2992,2995,2998,3001,3004],{"className":2982},[641],[580,2984],{"className":2985,"style":1482},[645],[580,2987,604],{"className":2988,"style":655},[650,654],[580,2990,614],{"className":2991},[697],[580,2993,1926],{"className":2994},[650],[580,2996,620],{"className":2997},[704],[580,2999],{"className":3000,"style":709},[708],[580,3002,1462],{"className":3003},[713],[580,3005],{"className":3006,"style":709},[708],[580,3008,3010,3013,3016],{"className":3009},[641],[580,3011],{"className":3012,"style":2159},[645],[580,3014,1779],{"className":3015},[650],[580,3017,1909],{"className":3018},[650],". Die Randpunkte darf man den Intervallen zurechnen, weil ",[580,3021,3023,3036],{"className":3022},[583],[580,3024,3026],{"className":3025},[587],[589,3027,3028],{"xmlns":591},[593,3029,3030,3034],{},[596,3031,3032],{},[602,3033,604],{},[629,3035,604],{"encoding":631},[580,3037,3039],{"className":3038,"ariaHidden":637},[636],[580,3040,3042,3045],{"className":3041},[641],[580,3043],{"className":3044,"style":810},[645],[580,3046,604],{"className":3047,"style":655},[650,654]," dort stetig ist.",[565,3050,3051,3146,3147,2166,3304,3403,3404,3432,3433,3461],{},[580,3052,3054,3081],{"className":3053},[583],[580,3055,3057],{"className":3056},[587],[589,3058,3059],{"xmlns":591},[593,3060,3061,3079],{},[596,3062,3063,3065,3067,3069,3071,3073],{},[602,3064,604],{},[606,3066,614],{"stretchy":613},[602,3068,617],{},[606,3070,620],{"stretchy":613},[606,3072,1462],{},[599,3074,3075,3077],{},[602,3076,617],{},[625,3078,1469],{},[629,3080,1472],{"encoding":631},[580,3082,3084,3111],{"className":3083,"ariaHidden":637},[636],[580,3085,3087,3090,3093,3096,3099,3102,3105,3108],{"className":3086},[641],[580,3088],{"className":3089,"style":1482},[645],[580,3091,604],{"className":3092,"style":655},[650,654],[580,3094,614],{"className":3095},[697],[580,3097,617],{"className":3098},[650,654],[580,3100,620],{"className":3101},[704],[580,3103],{"className":3104,"style":709},[708],[580,3106,1462],{"className":3107},[713],[580,3109],{"className":3110,"style":709},[708],[580,3112,3114,3117],{"className":3113},[641],[580,3115],{"className":3116,"style":1510},[645],[580,3118,3120,3123],{"className":3119},[650],[580,3121,617],{"className":3122},[650,654],[580,3124,3126],{"className":3125},[659],[580,3127,3129],{"className":3128},[663],[580,3130,3132],{"className":3131},[667],[580,3133,3135],{"className":3134,"style":1510},[671],[580,3136,3137,3140],{"style":675},[580,3138],{"className":3139,"style":680},[679],[580,3141,3143],{"className":3142},[684,685,686,687],[580,3144,1469],{"className":3145},[650,687]," hat ",[580,3148,3150,3188],{"className":3149},[583],[580,3151,3153],{"className":3152},[587],[589,3154,3155],{"xmlns":591},[593,3156,3157,3185],{},[596,3158,3159,3165,3167,3169,3171,3173,3175,3181,3183],{},[599,3160,3161,3163],{},[602,3162,604],{},[606,3164,610],{"mathvariant":608,"lspace":609,"rspace":609},[606,3166,614],{"stretchy":613},[602,3168,617],{},[606,3170,620],{"stretchy":613},[606,3172,1462],{},[625,3174,1469],{},[599,3176,3177,3179],{},[602,3178,617],{},[625,3180,1909],{},[606,3182,1087],{},[625,3184,627],{},[629,3186,3187],{"encoding":631},"f'(x) = 3x^2 \\geq 0",[580,3189,3191,3247,3295],{"className":3190,"ariaHidden":637},[636],[580,3192,3194,3197,3229,3232,3235,3238,3241,3244],{"className":3193},[641],[580,3195],{"className":3196,"style":646},[645],[580,3198,3200,3203],{"className":3199},[650],[580,3201,604],{"className":3202,"style":655},[650,654],[580,3204,3206],{"className":3205},[659],[580,3207,3209],{"className":3208},[663],[580,3210,3212],{"className":3211},[667],[580,3213,3215],{"className":3214,"style":672},[671],[580,3216,3217,3220],{"style":675},[580,3218],{"className":3219,"style":680},[679],[580,3221,3223],{"className":3222},[684,685,686,687],[580,3224,3226],{"className":3225},[650,687],[580,3227,610],{"className":3228},[650,687],[580,3230,614],{"className":3231},[697],[580,3233,617],{"className":3234},[650,654],[580,3236,620],{"className":3237},[704],[580,3239],{"className":3240,"style":709},[708],[580,3242,1462],{"className":3243},[713],[580,3245],{"className":3246,"style":709},[708],[580,3248,3250,3254,3257,3286,3289,3292],{"className":3249},[641],[580,3251],{"className":3252,"style":3253},[645],"height:0.9501em;vertical-align:-0.136em;",[580,3255,1469],{"className":3256},[650],[580,3258,3260,3263],{"className":3259},[650],[580,3261,617],{"className":3262},[650,654],[580,3264,3266],{"className":3265},[659],[580,3267,3269],{"className":3268},[663],[580,3270,3272],{"className":3271},[667],[580,3273,3275],{"className":3274,"style":1510},[671],[580,3276,3277,3280],{"style":675},[580,3278],{"className":3279,"style":680},[679],[580,3281,3283],{"className":3282},[684,685,686,687],[580,3284,1909],{"className":3285},[650,687],[580,3287],{"className":3288,"style":709},[708],[580,3290,1087],{"className":3291},[713],[580,3293],{"className":3294,"style":709},[708],[580,3296,3298,3301],{"className":3297},[641],[580,3299],{"className":3300,"style":723},[645],[580,3302,627],{"className":3303},[650],[580,3305,3307,3335],{"className":3306},[583],[580,3308,3310],{"className":3309},[587],[589,3311,3312],{"xmlns":591},[593,3313,3314,3332],{},[596,3315,3316,3322,3324,3326,3328,3330],{},[599,3317,3318,3320],{},[602,3319,604],{},[606,3321,610],{"mathvariant":608,"lspace":609,"rspace":609},[606,3323,614],{"stretchy":613},[625,3325,627],{},[606,3327,620],{"stretchy":613},[606,3329,1462],{},[625,3331,627],{},[629,3333,3334],{"encoding":631},"f'(0) = 0",[580,3336,3338,3394],{"className":3337,"ariaHidden":637},[636],[580,3339,3341,3344,3376,3379,3382,3385,3388,3391],{"className":3340},[641],[580,3342],{"className":3343,"style":646},[645],[580,3345,3347,3350],{"className":3346},[650],[580,3348,604],{"className":3349,"style":655},[650,654],[580,3351,3353],{"className":3352},[659],[580,3354,3356],{"className":3355},[663],[580,3357,3359],{"className":3358},[667],[580,3360,3362],{"className":3361,"style":672},[671],[580,3363,3364,3367],{"style":675},[580,3365],{"className":3366,"style":680},[679],[580,3368,3370],{"className":3369},[684,685,686,687],[580,3371,3373],{"className":3372},[650,687],[580,3374,610],{"className":3375},[650,687],[580,3377,614],{"className":3378},[697],[580,3380,627],{"className":3381},[650],[580,3383,620],{"className":3384},[704],[580,3386],{"className":3387,"style":709},[708],[580,3389,1462],{"className":3390},[713],[580,3392],{"className":3393,"style":709},[708],[580,3395,3397,3400],{"className":3396},[641],[580,3398],{"className":3399,"style":723},[645],[580,3401,627],{"className":3402},[650],". Trotzdem ist ",[580,3405,3407,3420],{"className":3406},[583],[580,3408,3410],{"className":3409},[587],[589,3411,3412],{"xmlns":591},[593,3413,3414,3418],{},[596,3415,3416],{},[602,3417,604],{},[629,3419,604],{"encoding":631},[580,3421,3423],{"className":3422,"ariaHidden":637},[636],[580,3424,3426,3429],{"className":3425},[641],[580,3427],{"className":3428,"style":810},[645],[580,3430,604],{"className":3431,"style":655},[650,654]," auf ganz ",[580,3434,3436,3449],{"className":3435},[583],[580,3437,3439],{"className":3438},[587],[589,3440,3441],{"xmlns":591},[593,3442,3443,3447],{},[596,3444,3445],{},[602,3446,1558],{"mathvariant":1557},[629,3448,2212],{"encoding":631},[580,3450,3452],{"className":3451,"ariaHidden":637},[636],[580,3453,3455,3458],{"className":3454},[641],[580,3456],{"className":3457,"style":2222},[645],[580,3459,1558],{"className":3460},[650,1585]," streng monoton wachsend.",[560,3463,3465],{"id":3464},"typische-fehler","Typische Fehler",[574,3467,3468,4128,4364],{},[577,3469,3470,3471,3620,3621,3851,3852,3987,3988,4016,4017,4074,4075,4127],{},"Das Kriterium über Definitionslücken hinweg anwenden. Für ",[580,3472,3474,3503],{"className":3473},[583],[580,3475,3477],{"className":3476},[587],[589,3478,3479],{"xmlns":591},[593,3480,3481,3500],{},[596,3482,3483,3485,3487,3489,3491,3493],{},[602,3484,604],{},[606,3486,614],{"stretchy":613},[602,3488,617],{},[606,3490,620],{"stretchy":613},[606,3492,1462],{},[3494,3495,3496,3498],"mfrac",{},[625,3497,1926],{},[602,3499,617],{},[629,3501,3502],{"encoding":631},"f(x) = \\frac{1}{x}",[580,3504,3506,3533],{"className":3505,"ariaHidden":637},[636],[580,3507,3509,3512,3515,3518,3521,3524,3527,3530],{"className":3508},[641],[580,3510],{"className":3511,"style":1482},[645],[580,3513,604],{"className":3514,"style":655},[650,654],[580,3516,614],{"className":3517},[697],[580,3519,617],{"className":3520},[650,654],[580,3522,620],{"className":3523},[704],[580,3525],{"className":3526,"style":709},[708],[580,3528,1462],{"className":3529},[713],[580,3531],{"className":3532,"style":709},[708],[580,3534,3536,3540],{"className":3535},[641],[580,3537],{"className":3538,"style":3539},[645],"height:1.1901em;vertical-align:-0.345em;",[580,3541,3543,3547,3617],{"className":3542},[650],[580,3544],{"className":3545},[697,3546],"nulldelimiter",[580,3548,3550],{"className":3549},[3494],[580,3551,3554,3608],{"className":3552},[663,3553],"vlist-t2",[580,3555,3557,3603],{"className":3556},[667],[580,3558,3561,3577,3588],{"className":3559,"style":3560},[671],"height:0.8451em;",[580,3562,3564,3568],{"style":3563},"top:-2.655em;",[580,3565],{"className":3566,"style":3567},[679],"height:3em;",[580,3569,3571],{"className":3570},[684,685,686,687],[580,3572,3574],{"className":3573},[650,687],[580,3575,617],{"className":3576},[650,654,687],[580,3578,3580,3583],{"style":3579},"top:-3.23em;",[580,3581],{"className":3582,"style":3567},[679],[580,3584],{"className":3585,"style":3587},[3586],"frac-line","border-bottom-width:0.04em;",[580,3589,3591,3594],{"style":3590},"top:-3.394em;",[580,3592],{"className":3593,"style":3567},[679],[580,3595,3597],{"className":3596},[684,685,686,687],[580,3598,3600],{"className":3599},[650,687],[580,3601,1926],{"className":3602},[650,687],[580,3604,3607],{"className":3605},[3606],"vlist-s","​",[580,3609,3611],{"className":3610},[667],[580,3612,3615],{"className":3613,"style":3614},[671],"height:0.345em;",[580,3616],{},[580,3618],{"className":3619},[704,3546]," ist ",[580,3622,3624,3666],{"className":3623},[583],[580,3625,3627],{"className":3626},[587],[589,3628,3629],{"xmlns":591},[593,3630,3631,3663],{},[596,3632,3633,3639,3641,3643,3645,3647,3649,3659,3661],{},[599,3634,3635,3637],{},[602,3636,604],{},[606,3638,610],{"mathvariant":608,"lspace":609,"rspace":609},[606,3640,614],{"stretchy":613},[602,3642,617],{},[606,3644,620],{"stretchy":613},[606,3646,1462],{},[606,3648,1779],{},[3494,3650,3651,3653],{},[625,3652,1926],{},[599,3654,3655,3657],{},[602,3656,617],{},[625,3658,1909],{},[606,3660,876],{},[625,3662,627],{},[629,3664,3665],{"encoding":631},"f'(x) = -\\frac{1}{x^2} \u003C 0",[580,3667,3669,3725,3842],{"className":3668,"ariaHidden":637},[636],[580,3670,3672,3675,3707,3710,3713,3716,3719,3722],{"className":3671},[641],[580,3673],{"className":3674,"style":646},[645],[580,3676,3678,3681],{"className":3677},[650],[580,3679,604],{"className":3680,"style":655},[650,654],[580,3682,3684],{"className":3683},[659],[580,3685,3687],{"className":3686},[663],[580,3688,3690],{"className":3689},[667],[580,3691,3693],{"className":3692,"style":672},[671],[580,3694,3695,3698],{"style":675},[580,3696],{"className":3697,"style":680},[679],[580,3699,3701],{"className":3700},[684,685,686,687],[580,3702,3704],{"className":3703},[650,687],[580,3705,610],{"className":3706},[650,687],[580,3708,614],{"className":3709},[697],[580,3711,617],{"className":3712},[650,654],[580,3714,620],{"className":3715},[704],[580,3717],{"className":3718,"style":709},[708],[580,3720,1462],{"className":3721},[713],[580,3723],{"className":3724,"style":709},[708],[580,3726,3728,3731,3734,3833,3836,3839],{"className":3727},[641],[580,3729],{"className":3730,"style":3539},[645],[580,3732,1779],{"className":3733},[650],[580,3735,3737,3740,3830],{"className":3736},[650],[580,3738],{"className":3739},[697,3546],[580,3741,3743],{"className":3742},[3494],[580,3744,3746,3822],{"className":3745},[663,3553],[580,3747,3749,3819],{"className":3748},[667],[580,3750,3752,3797,3805],{"className":3751,"style":3560},[671],[580,3753,3754,3757],{"style":3563},[580,3755],{"className":3756,"style":3567},[679],[580,3758,3760],{"className":3759},[684,685,686,687],[580,3761,3763],{"className":3762},[650,687],[580,3764,3766,3769],{"className":3765},[650,687],[580,3767,617],{"className":3768},[650,654,687],[580,3770,3772],{"className":3771},[659],[580,3773,3775],{"className":3774},[663],[580,3776,3778],{"className":3777},[667],[580,3779,3782],{"className":3780,"style":3781},[671],"height:0.7463em;",[580,3783,3785,3789],{"style":3784},"top:-2.786em;margin-right:0.0714em;",[580,3786],{"className":3787,"style":3788},[679],"height:2.5em;",[580,3790,3794],{"className":3791},[684,3792,3793,687],"reset-size3","size1",[580,3795,1909],{"className":3796},[650,687],[580,3798,3799,3802],{"style":3579},[580,3800],{"className":3801,"style":3567},[679],[580,3803],{"className":3804,"style":3587},[3586],[580,3806,3807,3810],{"style":3590},[580,3808],{"className":3809,"style":3567},[679],[580,3811,3813],{"className":3812},[684,685,686,687],[580,3814,3816],{"className":3815},[650,687],[580,3817,1926],{"className":3818},[650,687],[580,3820,3607],{"className":3821},[3606],[580,3823,3825],{"className":3824},[667],[580,3826,3828],{"className":3827,"style":3614},[671],[580,3829],{},[580,3831],{"className":3832},[704,3546],[580,3834],{"className":3835,"style":709},[708],[580,3837,876],{"className":3838},[713],[580,3840],{"className":3841,"style":709},[708],[580,3843,3845,3848],{"className":3844},[641],[580,3846],{"className":3847,"style":723},[645],[580,3849,627],{"className":3850},[650],", aber ",[580,3853,3855,3897],{"className":3854},[583],[580,3856,3858],{"className":3857},[587],[589,3859,3860],{"xmlns":591},[593,3861,3862,3894],{},[596,3863,3864,3866,3868,3870,3872,3874,3876,3878,3880,3882,3884,3886,3888,3890,3892],{},[602,3865,604],{},[606,3867,614],{"stretchy":613},[606,3869,1779],{},[625,3871,1926],{},[606,3873,620],{"stretchy":613},[606,3875,1462],{},[606,3877,1779],{},[625,3879,1926],{},[606,3881,876],{},[602,3883,604],{},[606,3885,614],{"stretchy":613},[625,3887,1926],{},[606,3889,620],{"stretchy":613},[606,3891,1462],{},[625,3893,1926],{},[629,3895,3896],{"encoding":631},"f(-1) = -1 \u003C f(1) = 1",[580,3898,3900,3930,3951,3978],{"className":3899,"ariaHidden":637},[636],[580,3901,3903,3906,3909,3912,3915,3918,3921,3924,3927],{"className":3902},[641],[580,3904],{"className":3905,"style":1482},[645],[580,3907,604],{"className":3908,"style":655},[650,654],[580,3910,614],{"className":3911},[697],[580,3913,1779],{"className":3914},[650],[580,3916,1926],{"className":3917},[650],[580,3919,620],{"className":3920},[704],[580,3922],{"className":3923,"style":709},[708],[580,3925,1462],{"className":3926},[713],[580,3928],{"className":3929,"style":709},[708],[580,3931,3933,3936,3939,3942,3945,3948],{"className":3932},[641],[580,3934],{"className":3935,"style":2159},[645],[580,3937,1779],{"className":3938},[650],[580,3940,1926],{"className":3941},[650],[580,3943],{"className":3944,"style":709},[708],[580,3946,876],{"className":3947},[713],[580,3949],{"className":3950,"style":709},[708],[580,3952,3954,3957,3960,3963,3966,3969,3972,3975],{"className":3953},[641],[580,3955],{"className":3956,"style":1482},[645],[580,3958,604],{"className":3959,"style":655},[650,654],[580,3961,614],{"className":3962},[697],[580,3964,1926],{"className":3965},[650],[580,3967,620],{"className":3968},[704],[580,3970],{"className":3971,"style":709},[708],[580,3973,1462],{"className":3974},[713],[580,3976],{"className":3977,"style":709},[708],[580,3979,3981,3984],{"className":3980},[641],[580,3982],{"className":3983,"style":723},[645],[580,3985,1926],{"className":3986},[650],". ",[580,3989,3991,4004],{"className":3990},[583],[580,3992,3994],{"className":3993},[587],[589,3995,3996],{"xmlns":591},[593,3997,3998,4002],{},[596,3999,4000],{},[602,4001,604],{},[629,4003,604],{"encoding":631},[580,4005,4007],{"className":4006,"ariaHidden":637},[636],[580,4008,4010,4013],{"className":4009},[641],[580,4011],{"className":4012,"style":810},[645],[580,4014,604],{"className":4015,"style":655},[650,654]," fällt nur auf ",[580,4018,4020,4044],{"className":4019},[583],[580,4021,4023],{"className":4022},[587],[589,4024,4025],{"xmlns":591},[593,4026,4027,4041],{},[596,4028,4029,4031,4033,4035,4037,4039],{},[606,4030,614],{"stretchy":613},[606,4032,1779],{},[602,4034,2406],{"mathvariant":608},[606,4036,2409],{"separator":637},[625,4038,627],{},[606,4040,620],{"stretchy":613},[629,4042,4043],{"encoding":631},"(-\\infty, 0)",[580,4045,4047],{"className":4046,"ariaHidden":637},[636],[580,4048,4050,4053,4056,4059,4062,4065,4068,4071],{"className":4049},[641],[580,4051],{"className":4052,"style":1482},[645],[580,4054,614],{"className":4055},[697],[580,4057,1779],{"className":4058},[650],[580,4060,2406],{"className":4061},[650],[580,4063,2409],{"className":4064},[2441],[580,4066],{"className":4067,"style":2445},[708],[580,4069,627],{"className":4070},[650],[580,4072,620],{"className":4073},[704]," und auf ",[580,4076,4078,4100],{"className":4077},[583],[580,4079,4081],{"className":4080},[587],[589,4082,4083],{"xmlns":591},[593,4084,4085,4097],{},[596,4086,4087,4089,4091,4093,4095],{},[606,4088,614],{"stretchy":613},[625,4090,627],{},[606,4092,2409],{"separator":637},[602,4094,2406],{"mathvariant":608},[606,4096,620],{"stretchy":613},[629,4098,4099],{"encoding":631},"(0, \\infty)",[580,4101,4103],{"className":4102,"ariaHidden":637},[636],[580,4104,4106,4109,4112,4115,4118,4121,4124],{"className":4105},[641],[580,4107],{"className":4108,"style":1482},[645],[580,4110,614],{"className":4111},[697],[580,4113,627],{"className":4114},[650],[580,4116,2409],{"className":4117},[2441],[580,4119],{"className":4120,"style":2445},[708],[580,4122,2406],{"className":4123},[650],[580,4125,620],{"className":4126},[704]," jeweils einzeln.",[577,4129,4130,4131,4275,4276,4304,4305,847],{},"Aus ",[580,4132,4134,4167],{"className":4133},[583],[580,4135,4137],{"className":4136},[587],[589,4138,4139],{"xmlns":591},[593,4140,4141,4164],{},[596,4142,4143,4149,4151,4158,4160,4162],{},[599,4144,4145,4147],{},[602,4146,604],{},[606,4148,610],{"mathvariant":608,"lspace":609,"rspace":609},[606,4150,614],{"stretchy":613},[4152,4153,4154,4156],"msub",{},[602,4155,617],{},[625,4157,627],{},[606,4159,620],{"stretchy":613},[606,4161,1462],{},[625,4163,627],{},[629,4165,4166],{"encoding":631},"f'(x_0) = 0",[580,4168,4170,4266],{"className":4169,"ariaHidden":637},[636],[580,4171,4173,4176,4208,4211,4254,4257,4260,4263],{"className":4172},[641],[580,4174],{"className":4175,"style":646},[645],[580,4177,4179,4182],{"className":4178},[650],[580,4180,604],{"className":4181,"style":655},[650,654],[580,4183,4185],{"className":4184},[659],[580,4186,4188],{"className":4187},[663],[580,4189,4191],{"className":4190},[667],[580,4192,4194],{"className":4193,"style":672},[671],[580,4195,4196,4199],{"style":675},[580,4197],{"className":4198,"style":680},[679],[580,4200,4202],{"className":4201},[684,685,686,687],[580,4203,4205],{"className":4204},[650,687],[580,4206,610],{"className":4207},[650,687],[580,4209,614],{"className":4210},[697],[580,4212,4214,4217],{"className":4213},[650],[580,4215,617],{"className":4216},[650,654],[580,4218,4220],{"className":4219},[659],[580,4221,4223,4245],{"className":4222},[663,3553],[580,4224,4226,4242],{"className":4225},[667],[580,4227,4230],{"className":4228,"style":4229},[671],"height:0.3011em;",[580,4231,4233,4236],{"style":4232},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[580,4234],{"className":4235,"style":680},[679],[580,4237,4239],{"className":4238},[684,685,686,687],[580,4240,627],{"className":4241},[650,687],[580,4243,3607],{"className":4244},[3606],[580,4246,4248],{"className":4247},[667],[580,4249,4252],{"className":4250,"style":4251},[671],"height:0.15em;",[580,4253],{},[580,4255,620],{"className":4256},[704],[580,4258],{"className":4259,"style":709},[708],[580,4261,1462],{"className":4262},[713],[580,4264],{"className":4265,"style":709},[708],[580,4267,4269,4272],{"className":4268},[641],[580,4270],{"className":4271,"style":723},[645],[580,4273,627],{"className":4274},[650]," schließen, dass ",[580,4277,4279,4292],{"className":4278},[583],[580,4280,4282],{"className":4281},[587],[589,4283,4284],{"xmlns":591},[593,4285,4286,4290],{},[596,4287,4288],{},[602,4289,604],{},[629,4291,604],{"encoding":631},[580,4293,4295],{"className":4294,"ariaHidden":637},[636],[580,4296,4298,4301],{"className":4297},[641],[580,4299],{"className":4300,"style":810},[645],[580,4302,604],{"className":4303,"style":655},[650,654]," dort nicht streng monoton ist. Das zeigt ",[580,4306,4308,4326],{"className":4307},[583],[580,4309,4311],{"className":4310},[587],[589,4312,4313],{"xmlns":591},[593,4314,4315,4323],{},[596,4316,4317],{},[599,4318,4319,4321],{},[602,4320,617],{},[625,4322,1469],{},[629,4324,4325],{"encoding":631},"x^3",[580,4327,4329],{"className":4328,"ariaHidden":637},[636],[580,4330,4332,4335],{"className":4331},[641],[580,4333],{"className":4334,"style":1510},[645],[580,4336,4338,4341],{"className":4337},[650],[580,4339,617],{"className":4340},[650,654],[580,4342,4344],{"className":4343},[659],[580,4345,4347],{"className":4346},[663],[580,4348,4350],{"className":4349},[667],[580,4351,4353],{"className":4352,"style":1510},[671],[580,4354,4355,4358],{"style":675},[580,4356],{"className":4357,"style":680},[679],[580,4359,4361],{"className":4360},[684,685,686,687],[580,4362,1469],{"className":4363},[650,687],[577,4365,4366,4367,4395,4396,4457,4458,4524],{},"Das Vorzeichen von ",[580,4368,4370,4383],{"className":4369},[583],[580,4371,4373],{"className":4372},[587],[589,4374,4375],{"xmlns":591},[593,4376,4377,4381],{},[596,4378,4379],{},[602,4380,604],{},[629,4382,604],{"encoding":631},[580,4384,4386],{"className":4385,"ariaHidden":637},[636],[580,4387,4389,4392],{"className":4388},[641],[580,4390],{"className":4391,"style":810},[645],[580,4393,604],{"className":4394,"style":655},[650,654]," statt von ",[580,4397,4399,4416],{"className":4398},[583],[580,4400,4402],{"className":4401},[587],[589,4403,4404],{"xmlns":591},[593,4405,4406,4414],{},[596,4407,4408],{},[599,4409,4410,4412],{},[602,4411,604],{},[606,4413,610],{"mathvariant":608,"lspace":609,"rspace":609},[629,4415,1396],{"encoding":631},[580,4417,4419],{"className":4418,"ariaHidden":637},[636],[580,4420,4422,4425],{"className":4421},[641],[580,4423],{"className":4424,"style":1406},[645],[580,4426,4428,4431],{"className":4427},[650],[580,4429,604],{"className":4430,"style":655},[650,654],[580,4432,4434],{"className":4433},[659],[580,4435,4437],{"className":4436},[663],[580,4438,4440],{"className":4439},[667],[580,4441,4443],{"className":4442,"style":672},[671],[580,4444,4445,4448],{"style":675},[580,4446],{"className":4447,"style":680},[679],[580,4449,4451],{"className":4450},[684,685,686,687],[580,4452,4454],{"className":4453},[650,687],[580,4455,610],{"className":4456},[650,687]," untersuchen. ",[580,4459,4461,4485],{"className":4460},[583],[580,4462,4464],{"className":4463},[587],[589,4465,4466],{"xmlns":591},[593,4467,4468,4482],{},[596,4469,4470,4472,4474,4476,4478,4480],{},[602,4471,604],{},[606,4473,614],{"stretchy":613},[602,4475,617],{},[606,4477,620],{"stretchy":613},[606,4479,623],{},[625,4481,627],{},[629,4483,4484],{"encoding":631},"f(x) > 0",[580,4486,4488,4515],{"className":4487,"ariaHidden":637},[636],[580,4489,4491,4494,4497,4500,4503,4506,4509,4512],{"className":4490},[641],[580,4492],{"className":4493,"style":1482},[645],[580,4495,604],{"className":4496,"style":655},[650,654],[580,4498,614],{"className":4499},[697],[580,4501,617],{"className":4502},[650,654],[580,4504,620],{"className":4505},[704],[580,4507],{"className":4508,"style":709},[708],[580,4510,623],{"className":4511},[713],[580,4513],{"className":4514,"style":709},[708],[580,4516,4518,4521],{"className":4517},[641],[580,4519],{"className":4520,"style":723},[645],[580,4522,627],{"className":4523},[650]," sagt nichts über Steigen oder Fallen.",{"title":4526,"searchDepth":4527,"depth":4527,"links":4528},"",2,[4529,4530,4531],{"id":562,"depth":4527,"text":563},{"id":1745,"depth":4527,"text":1746},{"id":3464,"depth":4527,"text":3465},[4533,4536,4538,4541,4543,4545,4548,4550,4553],{"lhs":4534,"rhs":4535},"3*x^2 - 3","3*(x - 1)*(x + 1)",{"lhs":4537,"rhs":2261},"3*(-2)^2 - 3",{"lhs":4539,"rhs":4540},"3*0^2 - 3","-3",{"lhs":4542,"rhs":2261},"3*2^2 - 3",{"lhs":4544,"rhs":1909},"(-1)^3 - 3*(-1)",{"lhs":4546,"rhs":4547},"1^3 - 3*1","-2",{"lhs":4549,"rhs":627},"3*0^2",{"lhs":4551,"rhs":4552},"-1\u002Fx^2","-(1\u002Fx)^2",{"lhs":4554,"rhs":2149},"1\u002F(-1)","f \\text{ differenzierbar auf dem Intervall } I","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">differenzierbar auf dem Intervall\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>I\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">I\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:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">I\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md",{"caption":4560,"x":4561,"y":4564,"unit":4567,"unitY":4568,"axes":4569,"items":4570},"Graph von f(x) = x³ − 3x, steigend für x \u003C −1 und x > 1 (f′ > 0), 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class=\"mord text\">\u003Cspan class=\"mord\"> auf \u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">I\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.1em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"col-align-l\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.6em;\">\u003Cspan style=\"top:-3.76em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\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 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