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Wann ist sein Flächeninhalt am größten?",[1107,1108,1109,1194,1360],"ul",{},[576,1110,1111,1112],{},"Hauptbedingung: ",[595,1113,1115,1140],{"className":1114},[598],[595,1116,1118],{"className":1117},[602],[604,1119,1120],{"xmlns":606},[608,1121,1122,1137],{},[611,1123,1124,1127,1129,1131,1134],{},[614,1125,1126],{},"A",[701,1128,717],{},[614,1130,616],{},[701,1132,1133],{},"⋅",[614,1135,1136],{},"y",[618,1138,1139],{"encoding":620},"A = x \\cdot y",[595,1141,1143,1162,1183],{"className":1142,"ariaHidden":625},[624],[595,1144,1146,1150,1153,1156,1159],{"className":1145},[629],[595,1147],{"className":1148,"style":1149},[633],"height:0.6833em;",[595,1151,1126],{"className":1152},[638,639],[595,1154],{"className":1155,"style":795},[794],[595,1157,717],{"className":1158},[799],[595,1160],{"className":1161,"style":795},[794],[595,1163,1165,1169,1172,1176,1180],{"className":1164},[629],[595,1166],{"className":1167,"style":1168},[633],"height:0.4445em;",[595,1170,616],{"className":1171},[638,639],[595,1173],{"className":1174,"style":1175},[794],"margin-right:0.2222em;",[595,1177,1133],{"className":1178},[1179],"mbin",[595,1181],{"className":1182,"style":1175},[794],[595,1184,1186,1190],{"className":1185},[629],[595,1187],{"className":1188,"style":1189},[633],"height:0.625em;vertical-align:-0.1944em;",[595,1191,1136],{"className":1192,"style":1193},[638,639],"margin-right:0.0359em;",[576,1195,1196,1197,1284,1285],{},"Nebenbedingung: ",[595,1198,1200,1228],{"className":1199},[598],[595,1201,1203],{"className":1202},[602],[604,1204,1205],{"xmlns":606},[608,1206,1207,1225],{},[611,1208,1209,1212,1214,1217,1219,1221,1223],{},[719,1210,1211],{},"2",[614,1213,616],{},[701,1215,1216],{},"+",[719,1218,1211],{},[614,1220,1136],{},[701,1222,717],{},[719,1224,1071],{},[618,1226,1227],{"encoding":620},"2x + 2y = 20",[595,1229,1231,1253,1275],{"className":1230,"ariaHidden":625},[624],[595,1232,1234,1238,1241,1244,1247,1250],{"className":1233},[629],[595,1235],{"className":1236,"style":1237},[633],"height:0.7278em;vertical-align:-0.0833em;",[595,1239,1211],{"className":1240},[638],[595,1242,616],{"className":1243},[638,639],[595,1245],{"className":1246,"style":1175},[794],[595,1248,1216],{"className":1249},[1179],[595,1251],{"className":1252,"style":1175},[794],[595,1254,1256,1260,1263,1266,1269,1272],{"className":1255},[629],[595,1257],{"className":1258,"style":1259},[633],"height:0.8389em;vertical-align:-0.1944em;",[595,1261,1211],{"className":1262},[638],[595,1264,1136],{"className":1265,"style":1193},[638,639],[595,1267],{"className":1268,"style":795},[794],[595,1270,717],{"className":1271},[799],[595,1273],{"className":1274,"style":795},[794],[595,1276,1278,1281],{"className":1277},[629],[595,1279],{"className":1280,"style":809},[633],[595,1282,1071],{"className":1283},[638],", also ",[595,1286,1288,1312],{"className":1287},[598],[595,1289,1291],{"className":1290},[602],[604,1292,1293],{"xmlns":606},[608,1294,1295,1309],{},[611,1296,1297,1299,1301,1304,1307],{},[614,1298,1136],{},[701,1300,717],{},[719,1302,1303],{},"10",[701,1305,1306],{},"−",[614,1308,616],{},[618,1310,1311],{"encoding":620},"y = 10 - x",[595,1313,1315,1333,1351],{"className":1314,"ariaHidden":625},[624],[595,1316,1318,1321,1324,1327,1330],{"className":1317},[629],[595,1319],{"className":1320,"style":1189},[633],[595,1322,1136],{"className":1323,"style":1193},[638,639],[595,1325],{"className":1326,"style":795},[794],[595,1328,717],{"className":1329},[799],[595,1331],{"className":1332,"style":795},[794],[595,1334,1336,1339,1342,1345,1348],{"className":1335},[629],[595,1337],{"className":1338,"style":1237},[633],[595,1340,1303],{"className":1341},[638],[595,1343],{"className":1344,"style":1175},[794],[595,1346,1306],{"className":1347},[1179],[595,1349],{"className":1350,"style":1175},[794],[595,1352,1354,1357],{"className":1353},[629],[595,1355],{"className":1356,"style":634},[633],[595,1358,616],{"className":1359},[638,639],[576,1361,1362,1363,1547,1548],{},"Zielfunktion: ",[595,1364,1366,1414],{"className":1365},[598],[595,1367,1369],{"className":1368},[602],[604,1370,1371],{"xmlns":606},[608,1372,1373,1411],{},[611,1374,1375,1377,1379,1381,1383,1385,1387,1389,1391,1393,1395,1397,1399,1401,1403,1405],{},[614,1376,1126],{},[701,1378,709],{"stretchy":708},[614,1380,616],{},[701,1382,714],{"stretchy":708},[701,1384,717],{},[614,1386,616],{},[701,1388,709],{"stretchy":708},[719,1390,1303],{},[701,1392,1306],{},[614,1394,616],{},[701,1396,714],{"stretchy":708},[701,1398,717],{},[719,1400,1303],{},[614,1402,616],{},[701,1404,1306],{},[695,1406,1407,1409],{},[614,1408,616],{},[719,1410,1211],{},[618,1412,1413],{"encoding":620},"A(x) = x(10 - x) = 10x - x^2",[595,1415,1417,1445,1469,1490,1511],{"className":1416,"ariaHidden":625},[624],[595,1418,1420,1424,1427,1430,1433,1436,1439,1442],{"className":1419},[629],[595,1421],{"className":1422,"style":1423},[633],"height:1em;vertical-align:-0.25em;",[595,1425,1126],{"className":1426},[638,639],[595,1428,709],{"className":1429},[783],[595,1431,616],{"className":1432},[638,639],[595,1434,714],{"className":1435},[790],[595,1437],{"className":1438,"style":795},[794],[595,1440,717],{"className":1441},[799],[595,1443],{"className":1444,"style":795},[794],[595,1446,1448,1451,1454,1457,1460,1463,1466],{"className":1447},[629],[595,1449],{"className":1450,"style":1423},[633],[595,1452,616],{"className":1453},[638,639],[595,1455,709],{"className":1456},[783],[595,1458,1303],{"className":1459},[638],[595,1461],{"className":1462,"style":1175},[794],[595,1464,1306],{"className":1465},[1179],[595,1467],{"className":1468,"style":1175},[794],[595,1470,1472,1475,1478,1481,1484,1487],{"className":1471},[629],[595,1473],{"className":1474,"style":1423},[633],[595,1476,616],{"className":1477},[638,639],[595,1479,714],{"className":1480},[790],[595,1482],{"className":1483,"style":795},[794],[595,1485,717],{"className":1486},[799],[595,1488],{"className":1489,"style":795},[794],[595,1491,1493,1496,1499,1502,1505,1508],{"className":1492},[629],[595,1494],{"className":1495,"style":1237},[633],[595,1497,1303],{"className":1498},[638],[595,1500,616],{"className":1501},[638,639],[595,1503],{"className":1504,"style":1175},[794],[595,1506,1306],{"className":1507},[1179],[595,1509],{"className":1510,"style":1175},[794],[595,1512,1514,1518],{"className":1513},[629],[595,1515],{"className":1516,"style":1517},[633],"height:0.8141em;",[595,1519,1521,1524],{"className":1520},[638],[595,1522,616],{"className":1523},[638,639],[595,1525,1527],{"className":1526},[745],[595,1528,1530],{"className":1529},[749],[595,1531,1533],{"className":1532},[753],[595,1534,1536],{"className":1535,"style":1517},[757],[595,1537,1538,1541],{"style":761},[595,1539],{"className":1540,"style":766},[765],[595,1542,1544],{"className":1543},[770,771,772,773],[595,1545,1211],{"className":1546},[638,773]," mit ",[595,1549,1551,1574],{"className":1550},[598],[595,1552,1554],{"className":1553},[602],[604,1555,1556],{"xmlns":606},[608,1557,1558,1571],{},[611,1559,1560,1562,1565,1567,1569],{},[719,1561,721],{},[701,1563,1564],{},"\u003C",[614,1566,616],{},[701,1568,1564],{},[719,1570,1303],{},[618,1572,1573],{"encoding":620},"0 \u003C x \u003C 10",[595,1575,1577,1596,1615],{"className":1576,"ariaHidden":625},[624],[595,1578,1580,1584,1587,1590,1593],{"className":1579},[629],[595,1581],{"className":1582,"style":1583},[633],"height:0.6835em;vertical-align:-0.0391em;",[595,1585,721],{"className":1586},[638],[595,1588],{"className":1589,"style":795},[794],[595,1591,1564],{"className":1592},[799],[595,1594],{"className":1595,"style":795},[794],[595,1597,1599,1603,1606,1609,1612],{"className":1598},[629],[595,1600],{"className":1601,"style":1602},[633],"height:0.5782em;vertical-align:-0.0391em;",[595,1604,616],{"className":1605},[638,639],[595,1607],{"className":1608,"style":795},[794],[595,1610,1564],{"className":1611},[799],[595,1613],{"className":1614,"style":795},[794],[595,1616,1618,1621],{"className":1617},[629],[595,1619],{"className":1620,"style":809},[633],[595,1622,1303],{"className":1623},[638],[565,1625,1626,1774,1775,1827,1828,1958,1959,2010,2011,1049],{},[595,1627,1629,1667],{"className":1628},[598],[595,1630,1632],{"className":1631},[602],[604,1633,1634],{"xmlns":606},[608,1635,1636,1664],{},[611,1637,1638,1644,1646,1648,1650,1652,1654,1656,1658,1660,1662],{},[695,1639,1640,1642],{},[614,1641,1126],{},[701,1643,705],{"mathvariant":703,"lspace":704,"rspace":704},[701,1645,709],{"stretchy":708},[614,1647,616],{},[701,1649,714],{"stretchy":708},[701,1651,717],{},[719,1653,1303],{},[701,1655,1306],{},[719,1657,1211],{},[614,1659,616],{},[701,1661,717],{},[719,1663,721],{},[618,1665,1666],{"encoding":620},"A'(x) = 10 - 2x = 0",[595,1668,1670,1726,1744,1765],{"className":1669,"ariaHidden":625},[624],[595,1671,1673,1676,1708,1711,1714,1717,1720,1723],{"className":1672},[629],[595,1674],{"className":1675,"style":734},[633],[595,1677,1679,1682],{"className":1678},[638],[595,1680,1126],{"className":1681},[638,639],[595,1683,1685],{"className":1684},[745],[595,1686,1688],{"className":1687},[749],[595,1689,1691],{"className":1690},[753],[595,1692,1694],{"className":1693,"style":758},[757],[595,1695,1696,1699],{"style":761},[595,1697],{"className":1698,"style":766},[765],[595,1700,1702],{"className":1701},[770,771,772,773],[595,1703,1705],{"className":1704},[638,773],[595,1706,705],{"className":1707},[638,773],[595,1709,709],{"className":1710},[783],[595,1712,616],{"className":1713},[638,639],[595,1715,714],{"className":1716},[790],[595,1718],{"className":1719,"style":795},[794],[595,1721,717],{"className":1722},[799],[595,1724],{"className":1725,"style":795},[794],[595,1727,1729,1732,1735,1738,1741],{"className":1728},[629],[595,1730],{"className":1731,"style":1237},[633],[595,1733,1303],{"className":1734},[638],[595,1736],{"className":1737,"style":1175},[794],[595,1739,1306],{"className":1740},[1179],[595,1742],{"className":1743,"style":1175},[794],[595,1745,1747,1750,1753,1756,1759,1762],{"className":1746},[629],[595,1748],{"className":1749,"style":809},[633],[595,1751,1211],{"className":1752},[638],[595,1754,616],{"className":1755},[638,639],[595,1757],{"className":1758,"style":795},[794],[595,1760,717],{"className":1761},[799],[595,1763],{"className":1764,"style":795},[794],[595,1766,1768,1771],{"className":1767},[629],[595,1769],{"className":1770,"style":809},[633],[595,1772,721],{"className":1773},[638]," ergibt ",[595,1776,1778,1797],{"className":1777},[598],[595,1779,1781],{"className":1780},[602],[604,1782,1783],{"xmlns":606},[608,1784,1785,1794],{},[611,1786,1787,1789,1791],{},[614,1788,616],{},[701,1790,717],{},[719,1792,1793],{},"5",[618,1795,1796],{"encoding":620},"x = 5",[595,1798,1800,1818],{"className":1799,"ariaHidden":625},[624],[595,1801,1803,1806,1809,1812,1815],{"className":1802},[629],[595,1804],{"className":1805,"style":634},[633],[595,1807,616],{"className":1808},[638,639],[595,1810],{"className":1811,"style":795},[794],[595,1813,717],{"className":1814},[799],[595,1816],{"className":1817,"style":795},[794],[595,1819,1821,1824],{"className":1820},[629],[595,1822],{"className":1823,"style":809},[633],[595,1825,1793],{"className":1826},[638],", und ",[595,1829,1831,1869],{"className":1830},[598],[595,1832,1834],{"className":1833},[602],[604,1835,1836],{"xmlns":606},[608,1837,1838,1866],{},[611,1839,1840,1850,1852,1854,1856,1858,1860,1862,1864],{},[695,1841,1842,1844],{},[614,1843,1126],{},[611,1845,1846,1848],{},[701,1847,705],{"mathvariant":703},[701,1849,705],{"mathvariant":703},[701,1851,709],{"stretchy":708},[719,1853,1793],{},[701,1855,714],{"stretchy":708},[701,1857,717],{},[701,1859,1306],{},[719,1861,1211],{},[701,1863,1564],{},[719,1865,721],{},[618,1867,1868],{"encoding":620},"A''(5) = -2 \u003C 0",[595,1870,1872,1928,1949],{"className":1871,"ariaHidden":625},[624],[595,1873,1875,1878,1910,1913,1916,1919,1922,1925],{"className":1874},[629],[595,1876],{"className":1877,"style":734},[633],[595,1879,1881,1884],{"className":1880},[638],[595,1882,1126],{"className":1883},[638,639],[595,1885,1887],{"className":1886},[745],[595,1888,1890],{"className":1889},[749],[595,1891,1893],{"className":1892},[753],[595,1894,1896],{"className":1895,"style":758},[757],[595,1897,1898,1901],{"style":761},[595,1899],{"className":1900,"style":766},[765],[595,1902,1904],{"className":1903},[770,771,772,773],[595,1905,1907],{"className":1906},[638,773],[595,1908,880],{"className":1909},[638,773],[595,1911,709],{"className":1912},[783],[595,1914,1793],{"className":1915},[638],[595,1917,714],{"className":1918},[790],[595,1920],{"className":1921,"style":795},[794],[595,1923,717],{"className":1924},[799],[595,1926],{"className":1927,"style":795},[794],[595,1929,1931,1934,1937,1940,1943,1946],{"className":1930},[629],[595,1932],{"className":1933,"style":1237},[633],[595,1935,1306],{"className":1936},[638],[595,1938,1211],{"className":1939},[638],[595,1941],{"className":1942,"style":795},[794],[595,1944,1564],{"className":1945},[799],[595,1947],{"className":1948,"style":795},[794],[595,1950,1952,1955],{"className":1951},[629],[595,1953],{"className":1954,"style":809},[633],[595,1956,721],{"className":1957},[638],". Mit ",[595,1960,1962,1980],{"className":1961},[598],[595,1963,1965],{"className":1964},[602],[604,1966,1967],{"xmlns":606},[608,1968,1969,1977],{},[611,1970,1971,1973,1975],{},[614,1972,1136],{},[701,1974,717],{},[719,1976,1793],{},[618,1978,1979],{"encoding":620},"y = 5",[595,1981,1983,2001],{"className":1982,"ariaHidden":625},[624],[595,1984,1986,1989,1992,1995,1998],{"className":1985},[629],[595,1987],{"className":1988,"style":1189},[633],[595,1990,1136],{"className":1991,"style":1193},[638,639],[595,1993],{"className":1994,"style":795},[794],[595,1996,717],{"className":1997},[799],[595,1999],{"className":2000,"style":795},[794],[595,2002,2004,2007],{"className":2003},[629],[595,2005],{"className":2006,"style":809},[633],[595,2008,1793],{"className":2009},[638]," ist das Rechteck ein Quadrat mit ",[595,2012,2014,2047],{"className":2013},[598],[595,2015,2017],{"className":2016},[602],[604,2018,2019],{"xmlns":606},[608,2020,2021,2044],{},[611,2022,2023,2025,2027,2029,2031,2033,2036,2038],{},[614,2024,1126],{},[701,2026,709],{"stretchy":708},[719,2028,1793],{},[701,2030,714],{"stretchy":708},[701,2032,717],{},[719,2034,2035],{},"25",[1073,2037,1075],{},[695,2039,2040,2042],{},[1073,2041,1078],{},[719,2043,1211],{},[618,2045,2046],{"encoding":620},"A(5) = 25\\,\\text{cm}^2",[595,2048,2050,2077],{"className":2049,"ariaHidden":625},[624],[595,2051,2053,2056,2059,2062,2065,2068,2071,2074],{"className":2052},[629],[595,2054],{"className":2055,"style":1423},[633],[595,2057,1126],{"className":2058},[638,639],[595,2060,709],{"className":2061},[783],[595,2063,1793],{"className":2064},[638],[595,2066,714],{"className":2067},[790],[595,2069],{"className":2070,"style":795},[794],[595,2072,717],{"className":2073},[799],[595,2075],{"className":2076,"style":795},[794],[595,2078,2080,2083,2086,2089],{"className":2079},[629],[595,2081],{"className":2082,"style":1517},[633],[595,2084,2035],{"className":2085},[638],[595,2087],{"className":2088,"style":1097},[794],[595,2090,2092,2098],{"className":2091},[638],[595,2093,2095],{"className":2094},[638,1101],[595,2096,1078],{"className":2097},[638],[595,2099,2101],{"className":2100},[745],[595,2102,2104],{"className":2103},[749],[595,2105,2107],{"className":2106},[753],[595,2108,2110],{"className":2109,"style":1517},[757],[595,2111,2112,2115],{"style":761},[595,2113],{"className":2114,"style":766},[765],[595,2116,2118],{"className":2117},[770,771,772,773],[595,2119,1211],{"className":2120},[638,773],[565,2122,2123,2124,2167,2168,2196,2197,2271],{},"Aus einem quadratischen Blech mit ",[595,2125,2127,2146],{"className":2126},[598],[595,2128,2130],{"className":2129},[602],[604,2131,2132],{"xmlns":606},[608,2133,2134,2143],{},[611,2135,2136,2139,2141],{},[719,2137,2138],{},"12",[1073,2140,1075],{},[1073,2142,1078],{},[618,2144,2145],{"encoding":620},"12\\,\\text{cm}",[595,2147,2149],{"className":2148,"ariaHidden":625},[624],[595,2150,2152,2155,2158,2161],{"className":2151},[629],[595,2153],{"className":2154,"style":809},[633],[595,2156,2138],{"className":2157},[638],[595,2159],{"className":2160,"style":1097},[794],[595,2162,2164],{"className":2163},[638,1101],[595,2165,1078],{"className":2166},[638]," Seitenlänge schneidet man an den Ecken Quadrate mit der Seitenlänge ",[595,2169,2171,2184],{"className":2170},[598],[595,2172,2174],{"className":2173},[602],[604,2175,2176],{"xmlns":606},[608,2177,2178,2182],{},[611,2179,2180],{},[614,2181,616],{},[618,2183,616],{"encoding":620},[595,2185,2187],{"className":2186,"ariaHidden":625},[624],[595,2188,2190,2193],{"className":2189},[629],[595,2191],{"className":2192,"style":634},[633],[595,2194,616],{"className":2195},[638,639]," aus und biegt die Ränder zu einer offenen Schachtel hoch. Ihr Volumen für ",[595,2198,2200,2223],{"className":2199},[598],[595,2201,2203],{"className":2202},[602],[604,2204,2205],{"xmlns":606},[608,2206,2207,2220],{},[611,2208,2209,2211,2213,2215,2217],{},[719,2210,721],{},[701,2212,1564],{},[614,2214,616],{},[701,2216,1564],{},[719,2218,2219],{},"6",[618,2221,2222],{"encoding":620},"0 \u003C x \u003C 6",[595,2224,2226,2244,2262],{"className":2225,"ariaHidden":625},[624],[595,2227,2229,2232,2235,2238,2241],{"className":2228},[629],[595,2230],{"className":2231,"style":1583},[633],[595,2233,721],{"className":2234},[638],[595,2236],{"className":2237,"style":795},[794],[595,2239,1564],{"className":2240},[799],[595,2242],{"className":2243,"style":795},[794],[595,2245,2247,2250,2253,2256,2259],{"className":2246},[629],[595,2248],{"className":2249,"style":1602},[633],[595,2251,616],{"className":2252},[638,639],[595,2254],{"className":2255,"style":795},[794],[595,2257,1564],{"className":2258},[799],[595,2260],{"className":2261,"style":795},[794],[595,2263,2265,2268],{"className":2264},[629],[595,2266],{"className":2267,"style":809},[633],[595,2269,2219],{"className":2270},[638]," ist",[595,2273,2276],{"className":2274},[2275],"katex-display",[595,2277,2279,2391],{"className":2278},[598],[595,2280,2282],{"className":2281},[602],[604,2283,2285],{"xmlns":606,"display":2284},"block",[608,2286,2287,2388],{},[2288,2289,2292,2342],"mtable",{"rowspacing":2290,"columnalign":2291,"columnspacing":704},"0.25em","right left",[2293,2294,2295,2312],"mtr",{},[2296,2297,2298],"mtd",{},[2299,2300,2301],"mstyle",{"scriptlevel":721,"displaystyle":625},[611,2302,2303,2306,2308,2310],{},[614,2304,2305],{},"V",[701,2307,709],{"stretchy":708},[614,2309,616],{},[701,2311,714],{"stretchy":708},[2296,2313,2314],{},[2299,2315,2316],{"scriptlevel":721,"displaystyle":625},[611,2317,2318,2320,2322,2324,2326,2328,2330,2332,2334,2336],{},[611,2319],{},[701,2321,717],{},[614,2323,616],{},[701,2325,1133],{},[701,2327,709],{"stretchy":708},[719,2329,2138],{},[701,2331,1306],{},[719,2333,1211],{},[614,2335,616],{},[695,2337,2338,2340],{},[701,2339,714],{"stretchy":708},[719,2341,1211],{},[2293,2343,2344,2350],{},[2296,2345,2346],{},[2299,2347,2348],{"scriptlevel":721,"displaystyle":625},[611,2349],{},[2296,2351,2352],{},[2299,2353,2354],{"scriptlevel":721,"displaystyle":625},[611,2355,2356,2358,2360,2363,2370,2372,2375,2381,2383,2386],{},[611,2357],{},[701,2359,717],{},[719,2361,2362],{},"4",[695,2364,2365,2367],{},[614,2366,616],{},[719,2368,2369],{},"3",[701,2371,1306],{},[719,2373,2374],{},"48",[695,2376,2377,2379],{},[614,2378,616],{},[719,2380,1211],{},[701,2382,1216],{},[719,2384,2385],{},"144",[614,2387,616],{},[618,2389,2390],{"encoding":620},"\\begin{aligned}\nV(x) &= x \\cdot (12 - 2x)^2 \\\\\n&= 4x^3 - 48x^2 + 144x\n\\end{aligned}",[595,2392,2394],{"className":2393,"ariaHidden":625},[624],[595,2395,2397,2401],{"className":2396},[629],[595,2398],{"className":2399,"style":2400},[633],"height:2.7482em;vertical-align:-1.1241em;",[595,2402,2404],{"className":2403},[638],[595,2405,2407,2464],{"className":2406},[2288],[595,2408,2411],{"className":2409},[2410],"col-align-r",[595,2412,2414,2455],{"className":2413},[749,994],[595,2415,2417,2452],{"className":2416},[753],[595,2418,2421,2443],{"className":2419,"style":2420},[757],"height:1.6241em;",[595,2422,2424,2428],{"style":2423},"top:-3.76em;",[595,2425],{"className":2426,"style":2427},[765],"height:3em;",[595,2429,2431,2434,2437,2440],{"className":2430},[638],[595,2432,2305],{"className":2433,"style":1175},[638,639],[595,2435,709],{"className":2436},[783],[595,2438,616],{"className":2439},[638,639],[595,2441,714],{"className":2442},[790],[595,2444,2446,2449],{"style":2445},"top:-2.2359em;",[595,2447],{"className":2448,"style":2427},[765],[595,2450],{"className":2451},[638],[595,2453,1018],{"className":2454},[1017],[595,2456,2458],{"className":2457},[753],[595,2459,2462],{"className":2460,"style":2461},[757],"height:1.1241em;",[595,2463],{},[595,2465,2468],{"className":2466},[2467],"col-align-l",[595,2469,2471,2672],{"className":2470},[749,994],[595,2472,2474,2669],{"className":2473},[753],[595,2475,2477,2561],{"className":2476,"style":2420},[757],[595,2478,2479,2482],{"style":2423},[595,2480],{"className":2481,"style":2427},[765],[595,2483,2485,2488,2491,2494,2497,2500,2503,2506,2509,2512,2515,2518,2521,2524,2527,2530],{"className":2484},[638],[595,2486],{"className":2487},[638],[595,2489],{"className":2490,"style":795},[794],[595,2492,717],{"className":2493},[799],[595,2495],{"className":2496,"style":795},[794],[595,2498,616],{"className":2499},[638,639],[595,2501],{"className":2502,"style":1175},[794],[595,2504,1133],{"className":2505},[1179],[595,2507],{"className":2508,"style":1175},[794],[595,2510,709],{"className":2511},[783],[595,2513,2138],{"className":2514},[638],[595,2516],{"className":2517,"style":1175},[794],[595,2519,1306],{"className":2520},[1179],[595,2522],{"className":2523,"style":1175},[794],[595,2525,1211],{"className":2526},[638],[595,2528,616],{"className":2529},[638,639],[595,2531,2533,2536],{"className":2532},[790],[595,2534,714],{"className":2535},[790],[595,2537,2539],{"className":2538},[745],[595,2540,2542],{"className":2541},[749],[595,2543,2545],{"className":2544},[753],[595,2546,2549],{"className":2547,"style":2548},[757],"height:0.8641em;",[595,2550,2552,2555],{"style":2551},"top:-3.113em;margin-right:0.05em;",[595,2553],{"className":2554,"style":766},[765],[595,2556,2558],{"className":2557},[770,771,772,773],[595,2559,1211],{"className":2560},[638,773],[595,2562,2563,2566],{"style":2445},[595,2564],{"className":2565,"style":2427},[765],[595,2567,2569,2572,2575,2578,2581,2584,2613,2616,2619,2622,2625,2654,2657,2660,2663,2666],{"className":2568},[638],[595,2570],{"className":2571},[638],[595,2573],{"className":2574,"style":795},[794],[595,2576,717],{"className":2577},[799],[595,2579],{"className":2580,"style":795},[794],[595,2582,2362],{"className":2583},[638],[595,2585,2587,2590],{"className":2586},[638],[595,2588,616],{"className":2589},[638,639],[595,2591,2593],{"className":2592},[745],[595,2594,2596],{"className":2595},[749],[595,2597,2599],{"className":2598},[753],[595,2600,2602],{"className":2601,"style":2548},[757],[595,2603,2604,2607],{"style":2551},[595,2605],{"className":2606,"style":766},[765],[595,2608,2610],{"className":2609},[770,771,772,773],[595,2611,2369],{"className":2612},[638,773],[595,2614],{"className":2615,"style":1175},[794],[595,2617,1306],{"className":2618},[1179],[595,2620],{"className":2621,"style":1175},[794],[595,2623,2374],{"className":2624},[638],[595,2626,2628,2631],{"className":2627},[638],[595,2629,616],{"className":2630},[638,639],[595,2632,2634],{"className":2633},[745],[595,2635,2637],{"className":2636},[749],[595,2638,2640],{"className":2639},[753],[595,2641,2643],{"className":2642,"style":2548},[757],[595,2644,2645,2648],{"style":2551},[595,2646],{"className":2647,"style":766},[765],[595,2649,2651],{"className":2650},[770,771,772,773],[595,2652,1211],{"className":2653},[638,773],[595,2655],{"className":2656,"style":1175},[794],[595,2658,1216],{"className":2659},[1179],[595,2661],{"className":2662,"style":1175},[794],[595,2664,2385],{"className":2665},[638],[595,2667,616],{"className":2668},[638,639],[595,2670,1018],{"className":2671},[1017],[595,2673,2675],{"className":2674},[753],[595,2676,2678],{"className":2677,"style":2461},[757],[595,2679],{},[565,2681,2682,2963,2964,1958,3015,3146,3147,3277,3278,3463,3464,1049],{},[595,2683,2685,2754],{"className":2684},[598],[595,2686,2688],{"className":2687},[602],[604,2689,2690],{"xmlns":606},[608,2691,2692,2751],{},[611,2693,2694,2700,2702,2704,2706,2708,2710,2716,2718,2721,2723,2725,2727,2729,2731,2733,2735,2737,2739,2741,2743,2745,2747,2749],{},[695,2695,2696,2698],{},[614,2697,2305],{},[701,2699,705],{"mathvariant":703,"lspace":704,"rspace":704},[701,2701,709],{"stretchy":708},[614,2703,616],{},[701,2705,714],{"stretchy":708},[701,2707,717],{},[719,2709,2138],{},[695,2711,2712,2714],{},[614,2713,616],{},[719,2715,1211],{},[701,2717,1306],{},[719,2719,2720],{},"96",[614,2722,616],{},[701,2724,1216],{},[719,2726,2385],{},[701,2728,717],{},[719,2730,2138],{},[701,2732,709],{"stretchy":708},[614,2734,616],{},[701,2736,1306],{},[719,2738,1211],{},[701,2740,714],{"stretchy":708},[701,2742,709],{"stretchy":708},[614,2744,616],{},[701,2746,1306],{},[719,2748,2219],{},[701,2750,714],{"stretchy":708},[618,2752,2753],{"encoding":620},"V'(x) = 12x^2 - 96x + 144 = 12(x - 2)(x - 6)",[595,2755,2757,2813,2861,2882,2900,2924,2951],{"className":2756,"ariaHidden":625},[624],[595,2758,2760,2763,2795,2798,2801,2804,2807,2810],{"className":2759},[629],[595,2761],{"className":2762,"style":734},[633],[595,2764,2766,2769],{"className":2765},[638],[595,2767,2305],{"className":2768,"style":1175},[638,639],[595,2770,2772],{"className":2771},[745],[595,2773,2775],{"className":2774},[749],[595,2776,2778],{"className":2777},[753],[595,2779,2781],{"className":2780,"style":758},[757],[595,2782,2783,2786],{"style":761},[595,2784],{"className":2785,"style":766},[765],[595,2787,2789],{"className":2788},[770,771,772,773],[595,2790,2792],{"className":2791},[638,773],[595,2793,705],{"className":2794},[638,773],[595,2796,709],{"className":2797},[783],[595,2799,616],{"className":2800},[638,639],[595,2802,714],{"className":2803},[790],[595,2805],{"className":2806,"style":795},[794],[595,2808,717],{"className":2809},[799],[595,2811],{"className":2812,"style":795},[794],[595,2814,2816,2820,2823,2852,2855,2858],{"className":2815},[629],[595,2817],{"className":2818,"style":2819},[633],"height:0.8974em;vertical-align:-0.0833em;",[595,2821,2138],{"className":2822},[638],[595,2824,2826,2829],{"className":2825},[638],[595,2827,616],{"className":2828},[638,639],[595,2830,2832],{"className":2831},[745],[595,2833,2835],{"className":2834},[749],[595,2836,2838],{"className":2837},[753],[595,2839,2841],{"className":2840,"style":1517},[757],[595,2842,2843,2846],{"style":761},[595,2844],{"className":2845,"style":766},[765],[595,2847,2849],{"className":2848},[770,771,772,773],[595,2850,1211],{"className":2851},[638,773],[595,2853],{"className":2854,"style":1175},[794],[595,2856,1306],{"className":2857},[1179],[595,2859],{"className":2860,"style":1175},[794],[595,2862,2864,2867,2870,2873,2876,2879],{"className":2863},[629],[595,2865],{"className":2866,"style":1237},[633],[595,2868,2720],{"className":2869},[638],[595,2871,616],{"className":2872},[638,639],[595,2874],{"className":2875,"style":1175},[794],[595,2877,1216],{"className":2878},[1179],[595,2880],{"className":2881,"style":1175},[794],[595,2883,2885,2888,2891,2894,2897],{"className":2884},[629],[595,2886],{"className":2887,"style":809},[633],[595,2889,2385],{"className":2890},[638],[595,2892],{"className":2893,"style":795},[794],[595,2895,717],{"className":2896},[799],[595,2898],{"className":2899,"style":795},[794],[595,2901,2903,2906,2909,2912,2915,2918,2921],{"className":2902},[629],[595,2904],{"className":2905,"style":1423},[633],[595,2907,2138],{"className":2908},[638],[595,2910,709],{"className":2911},[783],[595,2913,616],{"className":2914},[638,639],[595,2916],{"className":2917,"style":1175},[794],[595,2919,1306],{"className":2920},[1179],[595,2922],{"className":2923,"style":1175},[794],[595,2925,2927,2930,2933,2936,2939,2942,2945,2948],{"className":2926},[629],[595,2928],{"className":2929,"style":1423},[633],[595,2931,1211],{"className":2932},[638],[595,2934,714],{"className":2935},[790],[595,2937,709],{"className":2938},[783],[595,2940,616],{"className":2941},[638,639],[595,2943],{"className":2944,"style":1175},[794],[595,2946,1306],{"className":2947},[1179],[595,2949],{"className":2950,"style":1175},[794],[595,2952,2954,2957,2960],{"className":2953},[629],[595,2955],{"className":2956,"style":1423},[633],[595,2958,2219],{"className":2959},[638],[595,2961,714],{"className":2962},[790],". Im Definitionsbereich liegt nur ",[595,2965,2967,2985],{"className":2966},[598],[595,2968,2970],{"className":2969},[602],[604,2971,2972],{"xmlns":606},[608,2973,2974,2982],{},[611,2975,2976,2978,2980],{},[614,2977,616],{},[701,2979,717],{},[719,2981,1211],{},[618,2983,2984],{"encoding":620},"x = 2",[595,2986,2988,3006],{"className":2987,"ariaHidden":625},[624],[595,2989,2991,2994,2997,3000,3003],{"className":2990},[629],[595,2992],{"className":2993,"style":634},[633],[595,2995,616],{"className":2996},[638,639],[595,2998],{"className":2999,"style":795},[794],[595,3001,717],{"className":3002},[799],[595,3004],{"className":3005,"style":795},[794],[595,3007,3009,3012],{"className":3008},[629],[595,3010],{"className":3011,"style":809},[633],[595,3013,1211],{"className":3014},[638],[595,3016,3018,3057],{"className":3017},[598],[595,3019,3021],{"className":3020},[602],[604,3022,3023],{"xmlns":606},[608,3024,3025,3054],{},[611,3026,3027,3037,3039,3041,3043,3045,3048,3050,3052],{},[695,3028,3029,3031],{},[614,3030,2305],{},[611,3032,3033,3035],{},[701,3034,705],{"mathvariant":703},[701,3036,705],{"mathvariant":703},[701,3038,709],{"stretchy":708},[614,3040,616],{},[701,3042,714],{"stretchy":708},[701,3044,717],{},[719,3046,3047],{},"24",[614,3049,616],{},[701,3051,1306],{},[719,3053,2720],{},[618,3055,3056],{"encoding":620},"V''(x) = 24x - 96",[595,3058,3060,3116,3137],{"className":3059,"ariaHidden":625},[624],[595,3061,3063,3066,3098,3101,3104,3107,3110,3113],{"className":3062},[629],[595,3064],{"className":3065,"style":734},[633],[595,3067,3069,3072],{"className":3068},[638],[595,3070,2305],{"className":3071,"style":1175},[638,639],[595,3073,3075],{"className":3074},[745],[595,3076,3078],{"className":3077},[749],[595,3079,3081],{"className":3080},[753],[595,3082,3084],{"className":3083,"style":758},[757],[595,3085,3086,3089],{"style":761},[595,3087],{"className":3088,"style":766},[765],[595,3090,3092],{"className":3091},[770,771,772,773],[595,3093,3095],{"className":3094},[638,773],[595,3096,880],{"className":3097},[638,773],[595,3099,709],{"className":3100},[783],[595,3102,616],{"className":3103},[638,639],[595,3105,714],{"className":3106},[790],[595,3108],{"className":3109,"style":795},[794],[595,3111,717],{"className":3112},[799],[595,3114],{"className":3115,"style":795},[794],[595,3117,3119,3122,3125,3128,3131,3134],{"className":3118},[629],[595,3120],{"className":3121,"style":1237},[633],[595,3123,3047],{"className":3124},[638],[595,3126,616],{"className":3127},[638,639],[595,3129],{"className":3130,"style":1175},[794],[595,3132,1306],{"className":3133},[1179],[595,3135],{"className":3136,"style":1175},[794],[595,3138,3140,3143],{"className":3139},[629],[595,3141],{"className":3142,"style":809},[633],[595,3144,2720],{"className":3145},[638]," ist ",[595,3148,3150,3188],{"className":3149},[598],[595,3151,3153],{"className":3152},[602],[604,3154,3155],{"xmlns":606},[608,3156,3157,3185],{},[611,3158,3159,3169,3171,3173,3175,3177,3179,3181,3183],{},[695,3160,3161,3163],{},[614,3162,2305],{},[611,3164,3165,3167],{},[701,3166,705],{"mathvariant":703},[701,3168,705],{"mathvariant":703},[701,3170,709],{"stretchy":708},[719,3172,1211],{},[701,3174,714],{"stretchy":708},[701,3176,717],{},[701,3178,1306],{},[719,3180,2374],{},[701,3182,1564],{},[719,3184,721],{},[618,3186,3187],{"encoding":620},"V''(2) = -48 \u003C 0",[595,3189,3191,3247,3268],{"className":3190,"ariaHidden":625},[624],[595,3192,3194,3197,3229,3232,3235,3238,3241,3244],{"className":3193},[629],[595,3195],{"className":3196,"style":734},[633],[595,3198,3200,3203],{"className":3199},[638],[595,3201,2305],{"className":3202,"style":1175},[638,639],[595,3204,3206],{"className":3205},[745],[595,3207,3209],{"className":3208},[749],[595,3210,3212],{"className":3211},[753],[595,3213,3215],{"className":3214,"style":758},[757],[595,3216,3217,3220],{"style":761},[595,3218],{"className":3219,"style":766},[765],[595,3221,3223],{"className":3222},[770,771,772,773],[595,3224,3226],{"className":3225},[638,773],[595,3227,880],{"className":3228},[638,773],[595,3230,709],{"className":3231},[783],[595,3233,1211],{"className":3234},[638],[595,3236,714],{"className":3237},[790],[595,3239],{"className":3240,"style":795},[794],[595,3242,717],{"className":3243},[799],[595,3245],{"className":3246,"style":795},[794],[595,3248,3250,3253,3256,3259,3262,3265],{"className":3249},[629],[595,3251],{"className":3252,"style":1237},[633],[595,3254,1306],{"className":3255},[638],[595,3257,2374],{"className":3258},[638],[595,3260],{"className":3261,"style":795},[794],[595,3263,1564],{"className":3264},[799],[595,3266],{"className":3267,"style":795},[794],[595,3269,3271,3274],{"className":3270},[629],[595,3272],{"className":3273,"style":809},[633],[595,3275,721],{"className":3276},[638],", also ein Maximum mit ",[595,3279,3281,3327],{"className":3280},[598],[595,3282,3284],{"className":3283},[602],[604,3285,3286],{"xmlns":606},[608,3287,3288,3324],{},[611,3289,3290,3292,3294,3296,3298,3300,3302,3304,3311,3313,3316,3318],{},[614,3291,2305],{},[701,3293,709],{"stretchy":708},[719,3295,1211],{},[701,3297,714],{"stretchy":708},[701,3299,717],{},[719,3301,1211],{},[701,3303,1133],{},[695,3305,3306,3309],{},[719,3307,3308],{},"8",[719,3310,1211],{},[701,3312,717],{},[719,3314,3315],{},"128",[1073,3317,1075],{},[695,3319,3320,3322],{},[1073,3321,1078],{},[719,3323,2369],{},[618,3325,3326],{"encoding":620},"V(2) = 2 \\cdot 8^2 = 128\\,\\text{cm}^3",[595,3328,3330,3357,3375,3419],{"className":3329,"ariaHidden":625},[624],[595,3331,3333,3336,3339,3342,3345,3348,3351,3354],{"className":3332},[629],[595,3334],{"className":3335,"style":1423},[633],[595,3337,2305],{"className":3338,"style":1175},[638,639],[595,3340,709],{"className":3341},[783],[595,3343,1211],{"className":3344},[638],[595,3346,714],{"className":3347},[790],[595,3349],{"className":3350,"style":795},[794],[595,3352,717],{"className":3353},[799],[595,3355],{"className":3356,"style":795},[794],[595,3358,3360,3363,3366,3369,3372],{"className":3359},[629],[595,3361],{"className":3362,"style":809},[633],[595,3364,1211],{"className":3365},[638],[595,3367],{"className":3368,"style":1175},[794],[595,3370,1133],{"className":3371},[1179],[595,3373],{"className":3374,"style":1175},[794],[595,3376,3378,3381,3410,3413,3416],{"className":3377},[629],[595,3379],{"className":3380,"style":1517},[633],[595,3382,3384,3387],{"className":3383},[638],[595,3385,3308],{"className":3386},[638],[595,3388,3390],{"className":3389},[745],[595,3391,3393],{"className":3392},[749],[595,3394,3396],{"className":3395},[753],[595,3397,3399],{"className":3398,"style":1517},[757],[595,3400,3401,3404],{"style":761},[595,3402],{"className":3403,"style":766},[765],[595,3405,3407],{"className":3406},[770,771,772,773],[595,3408,1211],{"className":3409},[638,773],[595,3411],{"className":3412,"style":795},[794],[595,3414,717],{"className":3415},[799],[595,3417],{"className":3418,"style":795},[794],[595,3420,3422,3425,3428,3431],{"className":3421},[629],[595,3423],{"className":3424,"style":1517},[633],[595,3426,3315],{"className":3427},[638],[595,3429],{"className":3430,"style":1097},[794],[595,3432,3434,3440],{"className":3433},[638],[595,3435,3437],{"className":3436},[638,1101],[595,3438,1078],{"className":3439},[638],[595,3441,3443],{"className":3442},[745],[595,3444,3446],{"className":3445},[749],[595,3447,3449],{"className":3448},[753],[595,3450,3452],{"className":3451,"style":1517},[757],[595,3453,3454,3457],{"style":761},[595,3455],{"className":3456,"style":766},[765],[595,3458,3460],{"className":3459},[770,771,772,773],[595,3461,2369],{"className":3462},[638,773],". An den Rändern ist das Volumen ",[595,3465,3467,3480],{"className":3466},[598],[595,3468,3470],{"className":3469},[602],[604,3471,3472],{"xmlns":606},[608,3473,3474,3478],{},[611,3475,3476],{},[719,3477,721],{},[618,3479,721],{"encoding":620},[595,3481,3483],{"className":3482,"ariaHidden":625},[624],[595,3484,3486,3489],{"className":3485},[629],[595,3487],{"className":3488,"style":809},[633],[595,3490,721],{"className":3491},[638],[560,3493,3495],{"id":3494},"typische-fehler","Typische Fehler",[1107,3497,3498,3501,3556,3658],{},[576,3499,3500],{},"Die Hauptbedingung ableiten, solange sie noch zwei Variablen enthält. Erst die Nebenbedingung einsetzen.",[576,3502,3503,3504,3555],{},"Den Definitionsbereich vergessen und dadurch Lösungen wie ",[595,3505,3507,3525],{"className":3506},[598],[595,3508,3510],{"className":3509},[602],[604,3511,3512],{"xmlns":606},[608,3513,3514,3522],{},[611,3515,3516,3518,3520],{},[614,3517,616],{},[701,3519,717],{},[719,3521,2219],{},[618,3523,3524],{"encoding":620},"x = 6",[595,3526,3528,3546],{"className":3527,"ariaHidden":625},[624],[595,3529,3531,3534,3537,3540,3543],{"className":3530},[629],[595,3532],{"className":3533,"style":634},[633],[595,3535,616],{"className":3536},[638,639],[595,3538],{"className":3539,"style":795},[794],[595,3541,717],{"className":3542},[799],[595,3544],{"className":3545,"style":795},[794],[595,3547,3549,3552],{"className":3548},[629],[595,3550],{"className":3551,"style":809},[633],[595,3553,2219],{"className":3554},[638]," übernehmen, bei denen die Schachtel gar nicht existiert.",[576,3557,3558,3559,3657],{},"Nur ",[595,3560,3562,3589],{"className":3561},[598],[595,3563,3565],{"className":3564},[602],[604,3566,3567],{"xmlns":606},[608,3568,3569,3587],{},[611,3570,3571,3577,3579,3581,3583,3585],{},[695,3572,3573,3575],{},[614,3574,699],{},[701,3576,705],{"mathvariant":703,"lspace":704,"rspace":704},[701,3578,709],{"stretchy":708},[614,3580,616],{},[701,3582,714],{"stretchy":708},[701,3584,717],{},[719,3586,721],{},[618,3588,724],{"encoding":620},[595,3590,3592,3648],{"className":3591,"ariaHidden":625},[624],[595,3593,3595,3598,3630,3633,3636,3639,3642,3645],{"className":3594},[629],[595,3596],{"className":3597,"style":734},[633],[595,3599,3601,3604],{"className":3600},[638],[595,3602,699],{"className":3603,"style":741},[638,639],[595,3605,3607],{"className":3606},[745],[595,3608,3610],{"className":3609},[749],[595,3611,3613],{"className":3612},[753],[595,3614,3616],{"className":3615,"style":758},[757],[595,3617,3618,3621],{"style":761},[595,3619],{"className":3620,"style":766},[765],[595,3622,3624],{"className":3623},[770,771,772,773],[595,3625,3627],{"className":3626},[638,773],[595,3628,705],{"className":3629},[638,773],[595,3631,709],{"className":3632},[783],[595,3634,616],{"className":3635},[638,639],[595,3637,714],{"className":3638},[790],[595,3640],{"className":3641,"style":795},[794],[595,3643,717],{"className":3644},[799],[595,3646],{"className":3647,"style":795},[794],[595,3649,3651,3654],{"className":3650},[629],[595,3652],{"className":3653,"style":809},[633],[595,3655,721],{"className":3656},[638]," lösen, ohne zu prüfen, ob ein Maximum oder Minimum vorliegt, und ohne die Randwerte zu vergleichen.",[576,3659,3660],{},"Die Antwort unvollständig geben: Gefragt sind meist die Maße und der extremale Wert.",{"title":3662,"searchDepth":3663,"depth":3663,"links":3664},"",2,[3665,3666,3667],{"id":562,"depth":3663,"text":563},{"id":1052,"depth":3663,"text":1053},{"id":3494,"depth":3663,"text":3495},[3669,3672,3676,3678,3681,3684,3686,3689,3691],{"lhs":3670,"rhs":3671},"x*(10 - x)","10*x - x^2",{"lhs":3673,"rhs":721,"where":3674},"10 - 2*x",{"x":3675},5,{"lhs":3677,"rhs":2035},"5*(10 - 5)",{"lhs":3679,"rhs":3680},"x*(12 - 2*x)^2","4*x^3 - 48*x^2 + 144*x",{"lhs":3682,"rhs":3683},"12*x^2 - 96*x + 144","12*(x - 2)*(x - 6)",{"lhs":3685,"rhs":721},"round(((x+1e-5)*(12 - 2*(x+1e-5))^2 - (x-1e-5)*(12 - 2*(x-1e-5))^2)\u002F(2e-5) - (12*x^2 - 96*x + 144), 5)",{"lhs":3687,"rhs":3688},"24*2 - 96","-48",{"lhs":3690,"rhs":3315},"2*(12 - 2*2)^2",{"lhs":3692,"rhs":721},"6*(12 - 2*6)^2","Z \\text{ zweimal differenzierbar},\\ x_0 \\text{ im Inneren von } D_Z,\\ \\text{Randwerte zusätzlich prüfen}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>Z\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">Z\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:0.0715em;\">Z\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">zweimal\u003C\u002Fspan> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">differenzierbar\u003C\u002Fspan>\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">,\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:0.3em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x_0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\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>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">im Inneren von\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>D\u003C\u002Fmi>\u003Cmi>Z\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">D_Z,\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:0.8778em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">D\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3283em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0715em;\">Z\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=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">Randwerte zusätzlich 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153.82 39.33 L 154.73 39.9 L 155.65 40.51 L 156.57 41.14 L 157.48 41.81 L 158.4 42.5 L 159.32 43.22 L 160.23 43.98 L 161.15 44.76 L 162.07 45.57 L 162.98 46.41 L 163.9 47.28 L 164.82 48.18 L 165.73 49.11 L 166.65 50.07 L 167.57 51.06 L 168.48 52.08 L 169.4 53.13 L 170.32 54.2 L 171.23 55.31 L 172.15 56.45 L 173.07 57.61 L 173.98 58.81 L 174.9 60.03 L 175.82 61.29 L 176.73 62.57 L 177.65 63.88 L 178.57 65.23 L 179.48 66.6 L 180.4 68 L 181.32 69.43 L 182.23 70.89 L 183.15 72.38 L 184.07 73.9 L 184.98 75.45 L 185.9 77.03 L 186.82 78.64 L 187.73 80.28 L 188.65 81.95 L 189.57 83.64 L 190.48 85.37 L 191.4 87.13 L 192.32 88.91 L 193.23 90.73 L 194.15 92.57 L 195.07 94.44 L 195.98 96.35 L 196.9 98.28 L 197.82 100.24 L 198.73 102.24 L 199.65 104.26 L 200.57 106.31 L 201.48 108.39 L 202.4 110.5 L 203.32 112.64 L 204.23 114.81 L 205.15 117.01 L 206.07 119.24 L 206.98 121.49 L 207.9 123.78 L 208.82 126.1 L 209.73 128.44 L 210.65 130.82 L 211.57 133.23 L 212.48 135.66 L 213.4 138.13 L 214.32 140.62 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displaystyle=\"true\">\u003Cmrow>\u003Cmo>⇒\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmtext>lokales Maximum bei \u003C\u002Fmtext>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003C\u002Fmtable>\u003Cannotation encoding=\"application\u002Fx-tex\">\\begin{gathered} Z(x) = H\\big(x,\\ y(x)\\big) \\\\ Z'(x_0) = 0 \\;\\wedge\\; Z''(x_0) < 0 \\\\ \\Rightarrow\\; \\text{lokales Maximum bei } x_0 \\end{gathered}\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:4.21em;vertical-align:-1.855em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:2.355em;\">\u003Cspan 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style=\"margin-right:0.0359em;\">y\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"delimsizing size1\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.005em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">Z\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8019em;\">\u003Cspan style=\"top:-3.113em;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\">\u003Cspan class=\"mord mtight\">′\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\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=\"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>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">∧\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">Z\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8019em;\">\u003Cspan style=\"top:-3.113em;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\">\u003Cspan class=\"mord mtight\">′′\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\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=\"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>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-1.505em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\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>\u003Cspan class=\"mord text\">\u003Cspan class=\"mord\">lokales Maximum bei \u003C\u002Fspan>\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>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.855em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},"\u002Fde\u002Fformulas\u002Fmath\u002Fcalculus\u002Fextremwertaufgabe",[],[3745,3746,3747,3748],"extremum-condition","rectangle-area","curve-sketching","cuboid-volume",{"title":548,"description":3662},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fextremwertaufgabe","Man stellt eine Zielfunktion aus Haupt- und Nebenbedingung auf und bestimmt ihr Maximum oder Minimum mit der Ableitung.",[3753,3754,3755,3756,3757],"extremwertaufgabe","optimierung","zielfunktion","nebenbedingung","maximum",[3759,3763,3767,3771,3775],{"symbol":3760,"meaning":3761,"symbolHtml":3762},"H","Hauptbedingung, Formel für die Größe, die extremal werden soll","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>H\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">H\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:0.0813em;\">H\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3764,"meaning":3765,"symbolHtml":3766},"y(x)","aus der Nebenbedingung durch x ausgedrückte zweite Variable","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>y\u003C\u002Fmi>\u003Cmo 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