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0",[569,1157,1159,1230,1341,1430],{"className":1158,"ariaHidden":601},[617],[569,1160,1162,1165,1221,1224,1227],{"className":1161},[621],[569,1163],{"className":1164,"style":828},[625],[569,1166,1168,1171],{"className":1167},[630],[569,1169,590],{"className":1170,"style":632},[630,631],[569,1172,1175],{"className":1173},[1174],"msupsub",[569,1176,1180,1212],{"className":1177},[1178,1179],"vlist-t","vlist-t2",[569,1181,1184,1207],{"className":1182},[1183],"vlist-r",[569,1185,1189],{"className":1186,"style":1188},[1187],"vlist","height:0.1514em;",[569,1190,1192,1197],{"style":1191},"top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;",[569,1193],{"className":1194,"style":1196},[1195],"pstrut","height:2.7em;",[569,1198,1204],{"className":1199},[1200,1201,1202,1203],"sizing","reset-size6","size3","mtight",[569,1205,598],{"className":1206},[630,631,1203],[569,1208,1211],{"className":1209},[1210],"vlist-s","​",[569,1213,1215],{"className":1214},[1183],[569,1216,1219],{"className":1217,"style":1218},[1187],"height:0.15em;",[569,1220],{},[569,1222],{"className":1223,"style":784},[647],[569,1225,743],{"className":1226},[788],[569,1228],{"className":1229,"style":784},[647],[569,1231,1233,1237,1240,1281,1284,1288,1291,1332,1335,1338],{"className":1232},[621],[569,1234],{"className":1235,"style":1236},[625],"height:0.9805em;vertical-align:-0.2861em;",[569,1238,900],{"className":1239},[630,631],[569,1241,1243,1246],{"className":1242},[630],[569,1244,730],{"className":1245,"style":652},[630,631],[569,1247,1249],{"className":1248},[1174],[569,1250,1252,1273],{"className":1251},[1178,1179],[569,1253,1255,1270],{"className":1254},[1183],[569,1256,1258],{"className":1257,"style":1188},[1187],[569,1259,1261,1264],{"style":1260},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[569,1262],{"className":1263,"style":1196},[1195],[569,1265,1267],{"className":1266},[1200,1201,1202,1203],[569,1268,598],{"className":1269},[630,631,1203],[569,1271,1211],{"className":1272},[1210],[569,1274,1276],{"className":1275},[1183],[569,1277,1279],{"className":1278,"style":1218},[1187],[569,1280],{},[569,1282,602],{"className":1283},[643],[569,1285],{"className":1286,"style":1287},[647],"margin-right:2em;",[569,1289],{"className":1290,"style":648},[647],[569,1292,1294,1297],{"className":1293},[630],[569,1295,590],{"className":1296,"style":632},[630,631],[569,1298,1300],{"className":1299},[1174],[569,1301,1303,1323],{"className":1302},[1178,1179],[569,1304,1306,1320],{"className":1305},[1183],[569,1307,1309],{"className":1308,"style":1188},[1187],[569,1310,1311,1314],{"style":1191},[569,1312],{"className":1313,"style":1196},[1195],[569,1315,1317],{"className":1316},[1200,1201,1202,1203],[569,1318,605],{"className":1319,"style":652},[630,631,1203],[569,1321,1211],{"className":1322},[1210],[569,1324,1326],{"className":1325},[1183],[569,1327,1330],{"className":1328,"style":1329},[1187],"height:0.2861em;",[569,1331],{},[569,1333],{"className":1334,"style":784},[647],[569,1336,743],{"className":1337},[788],[569,1339],{"className":1340,"style":784},[647],[569,1342,1344,1348,1351,1391,1394,1397,1400,1403,1406,1409,1412,1415,1418,1421,1424,1427],{"className":1343},[621],[569,1345],{"className":1346,"style":1347},[625],"height:1.0361em;vertical-align:-0.2861em;",[569,1349,900],{"className":1350},[630,631],[569,1352,1354,1357],{"className":1353},[630],[569,1355,730],{"className":1356,"style":652},[630,631],[569,1358,1360],{"className":1359},[1174],[569,1361,1363,1383],{"className":1362},[1178,1179],[569,1364,1366,1380],{"className":1365},[1183],[569,1367,1369],{"className":1368,"style":1188},[1187],[569,1370,1371,1374],{"style":1260},[569,1372],{"className":1373,"style":1196},[1195],[569,1375,1377],{"className":1376},[1200,1201,1202,1203],[569,1378,605],{"className":1379,"style":652},[630,631,1203],[569,1381,1211],{"className":1382},[1210],[569,1384,1386],{"className":1385},[1183],[569,1387,1389],{"className":1388,"style":1329},[1187],[569,1390],{},[569,1392,602],{"className":1393},[643],[569,1395],{"className":1396,"style":1287},[647],[569,1398],{"className":1399,"style":648},[647],[569,1401,730],{"className":1402,"style":652},[630,631],[569,1404,595],{"className":1405},[636],[569,1407,598],{"className":1408},[630,631],[569,1410,602],{"className":1411},[643],[569,1413],{"className":1414,"style":648},[647],[569,1416,605],{"className":1417,"style":652},[630,631],[569,1419,608],{"className":1420},[656],[569,1422],{"className":1423,"style":784},[647],[569,1425,743],{"className":1426},[788],[569,1428],{"className":1429,"style":784},[647],[569,1431,1433,1436],{"className":1432},[621],[569,1434],{"className":1435,"style":798},[625],[569,1437,747],{"className":1438},[630],[565,1440,1441,1442,715,1444,1630,1631,1660],{},"Gleichwertig sucht man die kritischen Punkte der ",[712,1443,552],{},[569,1445,1447,1511],{"className":1446},[572],[569,1448,1450],{"className":1449},[576],[578,1451,1452],{"xmlns":580},[582,1453,1454,1508],{},[585,1455,1456,1459,1461,1463,1465,1467,1469,1471,1473,1475,1477,1479,1481,1483,1485,1487,1490,1492,1496,1498,1500,1502,1504,1506],{},[588,1457,1458],{},"L",[592,1460,595],{"stretchy":594},[588,1462,598],{},[592,1464,602],{"separator":601},[588,1466,605],{},[592,1468,602],{"separator":601},[588,1470,900],{},[592,1472,608],{"stretchy":594},[592,1474,743],{},[588,1476,590],{},[592,1478,595],{"stretchy":594},[588,1480,598],{},[592,1482,602],{"separator":601},[588,1484,605],{},[592,1486,608],{"stretchy":594},[592,1488,1489],{},"−",[588,1491,900],{},[1493,1494,1495],"mtext",{}," ",[588,1497,730],{},[592,1499,595],{"stretchy":594},[588,1501,598],{},[592,1503,602],{"separator":601},[588,1505,605],{},[592,1507,608],{"stretchy":594},[610,1509,1510],{"encoding":612},"L(x, y, \\lambda) = f(x, y) - \\lambda\\, g(x, y)",[569,1512,1514,1559,1597],{"className":1513,"ariaHidden":601},[617],[569,1515,1517,1520,1523,1526,1529,1532,1535,1538,1541,1544,1547,1550,1553,1556],{"className":1516},[621],[569,1518],{"className":1519,"style":626},[625],[569,1521,1458],{"className":1522},[630,631],[569,1524,595],{"className":1525},[636],[569,1527,598],{"className":1528},[630,631],[569,1530,602],{"className":1531},[643],[569,1533],{"className":1534,"style":648},[647],[569,1536,605],{"className":1537,"style":652},[630,631],[569,1539,602],{"className":1540},[643],[569,1542],{"className":1543,"style":648},[647],[569,1545,900],{"className":1546},[630,631],[569,1548,608],{"className":1549},[656],[569,1551],{"className":1552,"style":784},[647],[569,1554,743],{"className":1555},[788],[569,1557],{"className":1558,"style":784},[647],[569,1560,1562,1565,1568,1571,1574,1577,1580,1583,1586,1590,1594],{"className":1561},[621],[569,1563],{"className":1564,"style":626},[625],[569,1566,590],{"className":1567,"style":632},[630,631],[569,1569,595],{"className":1570},[636],[569,1572,598],{"className":1573},[630,631],[569,1575,602],{"className":1576},[643],[569,1578],{"className":1579,"style":648},[647],[569,1581,605],{"className":1582,"style":652},[630,631],[569,1584,608],{"className":1585},[656],[569,1587],{"className":1588,"style":1589},[647],"margin-right:0.2222em;",[569,1591,1489],{"className":1592},[1593],"mbin",[569,1595],{"className":1596,"style":1589},[647],[569,1598,1600,1603,1606,1609,1612,1615,1618,1621,1624,1627],{"className":1599},[621],[569,1601],{"className":1602,"style":626},[625],[569,1604,900],{"className":1605},[630,631],[569,1607],{"className":1608,"style":648},[647],[569,1610,730],{"className":1611,"style":652},[630,631],[569,1613,595],{"className":1614},[636],[569,1616,598],{"className":1617},[630,631],[569,1619,602],{"className":1620},[643],[569,1622],{"className":1623,"style":648},[647],[569,1625,605],{"className":1626,"style":652},[630,631],[569,1628,608],{"className":1629},[656],". Bei ",[569,1632,1634,1648],{"className":1633},[572],[569,1635,1637],{"className":1636},[576],[578,1638,1639],{"xmlns":580},[582,1640,1641,1646],{},[585,1642,1643],{},[588,1644,1645],{},"n",[610,1647,1645],{"encoding":612},[569,1649,1651],{"className":1650,"ariaHidden":601},[617],[569,1652,1654,1657],{"className":1653},[621],[569,1655],{"className":1656,"style":1015},[625],[569,1658,1645],{"className":1659},[630,631]," Variablen und mehreren Nebenbedingungen bekommt jede Nebenbedingung ihren eigenen Multiplikator.",[565,1662,1663,1664,1667,1668,1718,1719,1747],{},"Die Methode liefert nur ",[712,1665,1666],{},"Kandidaten",". Ist die Menge ",[569,1669,1671,1688],{"className":1670},[572],[569,1672,1674],{"className":1673},[576],[578,1675,1676],{"xmlns":580},[582,1677,1678,1686],{},[585,1679,1680,1682,1684],{},[588,1681,730],{},[592,1683,743],{},[745,1685,747],{},[610,1687,853],{"encoding":612},[569,1689,1691,1709],{"className":1690,"ariaHidden":601},[617],[569,1692,1694,1697,1700,1703,1706],{"className":1693},[621],[569,1695],{"className":1696,"style":863},[625],[569,1698,730],{"className":1699,"style":652},[630,631],[569,1701],{"className":1702,"style":784},[647],[569,1704,743],{"className":1705},[788],[569,1707],{"className":1708,"style":784},[647],[569,1710,1712,1715],{"className":1711},[621],[569,1713],{"className":1714,"style":798},[625],[569,1716,747],{"className":1717},[630]," beschränkt und abgeschlossen (z.B. ein Kreis), nimmt ",[569,1720,1722,1735],{"className":1721},[572],[569,1723,1725],{"className":1724},[576],[578,1726,1727],{"xmlns":580},[582,1728,1729,1733],{},[585,1730,1731],{},[588,1732,590],{},[610,1734,590],{"encoding":612},[569,1736,1738],{"className":1737,"ariaHidden":601},[617],[569,1739,1741,1744],{"className":1740},[621],[569,1742],{"className":1743,"style":828},[625],[569,1745,590],{"className":1746,"style":632},[630,631]," dort Maximum und Minimum an, und man vergleicht einfach die Funktionswerte der Kandidaten.",[560,1749,1751],{"id":1750},"beispiele","Beispiele",[565,1753,567,1754,1864,1865,2004,2005,1077],{},[569,1755,1757,1793],{"className":1756},[572],[569,1758,1760],{"className":1759},[576],[578,1761,1762],{"xmlns":580},[582,1763,1764,1790],{},[585,1765,1766,1768,1770,1772,1774,1776,1778,1780,1782,1785,1788],{},[588,1767,590],{},[592,1769,595],{"stretchy":594},[588,1771,598],{},[592,1773,602],{"separator":601},[588,1775,605],{},[592,1777,608],{"stretchy":594},[592,1779,743],{},[588,1781,598],{},[592,1783,1784],{},"+",[745,1786,1787],{},"2",[588,1789,605],{},[610,1791,1792],{"encoding":612},"f(x, y) = x + 2y",[569,1794,1796,1832,1851],{"className":1795,"ariaHidden":601},[617],[569,1797,1799,1802,1805,1808,1811,1814,1817,1820,1823,1826,1829],{"className":1798},[621],[569,1800],{"className":1801,"style":626},[625],[569,1803,590],{"className":1804,"style":632},[630,631],[569,1806,595],{"className":1807},[636],[569,1809,598],{"className":1810},[630,631],[569,1812,602],{"className":1813},[643],[569,1815],{"className":1816,"style":648},[647],[569,1818,605],{"className":1819,"style":652},[630,631],[569,1821,608],{"className":1822},[656],[569,1824],{"className":1825,"style":784},[647],[569,1827,743],{"className":1828},[788],[569,1830],{"className":1831,"style":784},[647],[569,1833,1835,1839,1842,1845,1848],{"className":1834},[621],[569,1836],{"className":1837,"style":1838},[625],"height:0.6667em;vertical-align:-0.0833em;",[569,1840,598],{"className":1841},[630,631],[569,1843],{"className":1844,"style":1589},[647],[569,1846,1784],{"className":1847},[1593],[569,1849],{"className":1850,"style":1589},[647],[569,1852,1854,1858,1861],{"className":1853},[621],[569,1855],{"className":1856,"style":1857},[625],"height:0.8389em;vertical-align:-0.1944em;",[569,1859,1787],{"className":1860},[630],[569,1862,605],{"className":1863,"style":652},[630,631]," auf dem Kreis ",[569,1866,1868,1900],{"className":1867},[572],[569,1869,1871],{"className":1870},[576],[578,1872,1873],{"xmlns":580},[582,1874,1875,1897],{},[585,1876,1877,1884,1886,1892,1894],{},[1878,1879,1880,1882],"msup",{},[588,1881,598],{},[745,1883,1787],{},[592,1885,1784],{},[1878,1887,1888,1890],{},[588,1889,605],{},[745,1891,1787],{},[592,1893,743],{},[745,1895,1896],{},"5",[610,1898,1899],{"encoding":612},"x^2 + y^2 = 5",[569,1901,1903,1950,1995],{"className":1902,"ariaHidden":601},[617],[569,1904,1906,1910,1941,1944,1947],{"className":1905},[621],[569,1907],{"className":1908,"style":1909},[625],"height:0.8974em;vertical-align:-0.0833em;",[569,1911,1913,1916],{"className":1912},[630],[569,1914,598],{"className":1915},[630,631],[569,1917,1919],{"className":1918},[1174],[569,1920,1922],{"className":1921},[1178],[569,1923,1925],{"className":1924},[1183],[569,1926,1929],{"className":1927,"style":1928},[1187],"height:0.8141em;",[569,1930,1932,1935],{"style":1931},"top:-3.063em;margin-right:0.05em;",[569,1933],{"className":1934,"style":1196},[1195],[569,1936,1938],{"className":1937},[1200,1201,1202,1203],[569,1939,1787],{"className":1940},[630,1203],[569,1942],{"className":1943,"style":1589},[647],[569,1945,1784],{"className":1946},[1593],[569,1948],{"className":1949,"style":1589},[647],[569,1951,1953,1957,1986,1989,1992],{"className":1952},[621],[569,1954],{"className":1955,"style":1956},[625],"height:1.0085em;vertical-align:-0.1944em;",[569,1958,1960,1963],{"className":1959},[630],[569,1961,605],{"className":1962,"style":652},[630,631],[569,1964,1966],{"className":1965},[1174],[569,1967,1969],{"className":1968},[1178],[569,1970,1972],{"className":1971},[1183],[569,1973,1975],{"className":1974,"style":1928},[1187],[569,1976,1977,1980],{"style":1931},[569,1978],{"className":1979,"style":1196},[1195],[569,1981,1983],{"className":1982},[1200,1201,1202,1203],[569,1984,1787],{"className":1985},[630,1203],[569,1987],{"className":1988,"style":784},[647],[569,1990,743],{"className":1991},[788],[569,1993],{"className":1994,"style":784},[647],[569,1996,1998,2001],{"className":1997},[621],[569,1999],{"className":2000,"style":798},[625],[569,2002,1896],{"className":2003},[630],", also mit ",[569,2006,2008,2052],{"className":2007},[572],[569,2009,2011],{"className":2010},[576],[578,2012,2013],{"xmlns":580},[582,2014,2015,2049],{},[585,2016,2017,2019,2021,2023,2025,2027,2029,2031,2037,2039,2045,2047],{},[588,2018,730],{},[592,2020,595],{"stretchy":594},[588,2022,598],{},[592,2024,602],{"separator":601},[588,2026,605],{},[592,2028,608],{"stretchy":594},[592,2030,743],{},[1878,2032,2033,2035],{},[588,2034,598],{},[745,2036,1787],{},[592,2038,1784],{},[1878,2040,2041,2043],{},[588,2042,605],{},[745,2044,1787],{},[592,2046,1489],{},[745,2048,1896],{},[610,2050,2051],{"encoding":612},"g(x, y) = x^2 + y^2 - 5",[569,2053,2055,2091,2135,2179],{"className":2054,"ariaHidden":601},[617],[569,2056,2058,2061,2064,2067,2070,2073,2076,2079,2082,2085,2088],{"className":2057},[621],[569,2059],{"className":2060,"style":626},[625],[569,2062,730],{"className":2063,"style":652},[630,631],[569,2065,595],{"className":2066},[636],[569,2068,598],{"className":2069},[630,631],[569,2071,602],{"className":2072},[643],[569,2074],{"className":2075,"style":648},[647],[569,2077,605],{"className":2078,"style":652},[630,631],[569,2080,608],{"className":2081},[656],[569,2083],{"className":2084,"style":784},[647],[569,2086,743],{"className":2087},[788],[569,2089],{"className":2090,"style":784},[647],[569,2092,2094,2097,2126,2129,2132],{"className":2093},[621],[569,2095],{"className":2096,"style":1909},[625],[569,2098,2100,2103],{"className":2099},[630],[569,2101,598],{"className":2102},[630,631],[569,2104,2106],{"className":2105},[1174],[569,2107,2109],{"className":2108},[1178],[569,2110,2112],{"className":2111},[1183],[569,2113,2115],{"className":2114,"style":1928},[1187],[569,2116,2117,2120],{"style":1931},[569,2118],{"className":2119,"style":1196},[1195],[569,2121,2123],{"className":2122},[1200,1201,1202,1203],[569,2124,1787],{"className":2125},[630,1203],[569,2127],{"className":2128,"style":1589},[647],[569,2130,1784],{"className":2131},[1593],[569,2133],{"className":2134,"style":1589},[647],[569,2136,2138,2141,2170,2173,2176],{"className":2137},[621],[569,2139],{"className":2140,"style":1956},[625],[569,2142,2144,2147],{"className":2143},[630],[569,2145,605],{"className":2146,"style":652},[630,631],[569,2148,2150],{"className":2149},[1174],[569,2151,2153],{"className":2152},[1178],[569,2154,2156],{"className":2155},[1183],[569,2157,2159],{"className":2158,"style":1928},[1187],[569,2160,2161,2164],{"style":1931},[569,2162],{"className":2163,"style":1196},[1195],[569,2165,2167],{"className":2166},[1200,1201,1202,1203],[569,2168,1787],{"className":2169},[630,1203],[569,2171],{"className":2172,"style":1589},[647],[569,2174,1489],{"className":2175},[1593],[569,2177],{"className":2178,"style":1589},[647],[569,2180,2182,2185],{"className":2181},[621],[569,2183],{"className":2184,"style":798},[625],[569,2186,1896],{"className":2187},[630],[569,2189,2191],{"className":2190},[1081],[569,2192,2194,2253],{"className":2193},[572],[569,2195,2197],{"className":2196},[576],[578,2198,2199],{"xmlns":580,"display":1090},[582,2200,2201,2250],{},[585,2202,2203,2206,2208,2210,2212,2214,2216,2218,2220,2222,2224,2226,2228,2230,2232,2238,2240,2246,2248],{},[745,2204,2205],{},"1",[592,2207,743],{},[745,2209,1787],{},[588,2211,900],{},[588,2213,598],{},[592,2215,602],{"separator":601},[647,2217],{"width":1116},[745,2219,1787],{},[592,2221,743],{},[745,2223,1787],{},[588,2225,900],{},[588,2227,605],{},[592,2229,602],{"separator":601},[647,2231],{"width":1116},[1878,2233,2234,2236],{},[588,2235,598],{},[745,2237,1787],{},[592,2239,1784],{},[1878,2241,2242,2244],{},[588,2243,605],{},[745,2245,1787],{},[592,2247,743],{},[745,2249,1896],{},[610,2251,2252],{"encoding":612},"1 = 2\\lambda x, \\qquad 2 = 2\\lambda y, \\qquad x^2 + y^2 = 5",[569,2254,2256,2274,2310,2375,2419],{"className":2255,"ariaHidden":601},[617],[569,2257,2259,2262,2265,2268,2271],{"className":2258},[621],[569,2260],{"className":2261,"style":798},[625],[569,2263,2205],{"className":2264},[630],[569,2266],{"className":2267,"style":784},[647],[569,2269,743],{"className":2270},[788],[569,2272],{"className":2273,"style":784},[647],[569,2275,2277,2280,2283,2286,2289,2292,2295,2298,2301,2304,2307],{"className":2276},[621],[569,2278],{"className":2279,"style":828},[625],[569,2281,1787],{"className":2282},[630],[569,2284,900],{"className":2285},[630,631],[569,2287,598],{"className":2288},[630,631],[569,2290,602],{"className":2291},[643],[569,2293],{"className":2294,"style":1287},[647],[569,2296],{"className":2297,"style":648},[647],[569,2299,1787],{"className":2300},[630],[569,2302],{"className":2303,"style":784},[647],[569,2305,743],{"className":2306},[788],[569,2308],{"className":2309,"style":784},[647],[569,2311,2313,2317,2320,2323,2326,2329,2332,2335,2366,2369,2372],{"className":2312},[621],[569,2314],{"className":2315,"style":2316},[625],"height:1.0585em;vertical-align:-0.1944em;",[569,2318,1787],{"className":2319},[630],[569,2321,900],{"className":2322},[630,631],[569,2324,605],{"className":2325,"style":652},[630,631],[569,2327,602],{"className":2328},[643],[569,2330],{"className":2331,"style":1287},[647],[569,2333],{"className":2334,"style":648},[647],[569,2336,2338,2341],{"className":2337},[630],[569,2339,598],{"className":2340},[630,631],[569,2342,2344],{"className":2343},[1174],[569,2345,2347],{"className":2346},[1178],[569,2348,2350],{"className":2349},[1183],[569,2351,2354],{"className":2352,"style":2353},[1187],"height:0.8641em;",[569,2355,2357,2360],{"style":2356},"top:-3.113em;margin-right:0.05em;",[569,2358],{"className":2359,"style":1196},[1195],[569,2361,2363],{"className":2362},[1200,1201,1202,1203],[569,2364,1787],{"className":2365},[630,1203],[569,2367],{"className":2368,"style":1589},[647],[569,2370,1784],{"className":2371},[1593],[569,2373],{"className":2374,"style":1589},[647],[569,2376,2378,2381,2410,2413,2416],{"className":2377},[621],[569,2379],{"className":2380,"style":2316},[625],[569,2382,2384,2387],{"className":2383},[630],[569,2385,605],{"className":2386,"style":652},[630,631],[569,2388,2390],{"className":2389},[1174],[569,2391,2393],{"className":2392},[1178],[569,2394,2396],{"className":2395},[1183],[569,2397,2399],{"className":2398,"style":2353},[1187],[569,2400,2401,2404],{"style":2356},[569,2402],{"className":2403,"style":1196},[1195],[569,2405,2407],{"className":2406},[1200,1201,1202,1203],[569,2408,1787],{"className":2409},[630,1203],[569,2411],{"className":2412,"style":784},[647],[569,2414,743],{"className":2415},[788],[569,2417],{"className":2418,"style":784},[647],[569,2420,2422,2425],{"className":2421},[621],[569,2423],{"className":2424,"style":798},[625],[569,2426,1896],{"className":2427},[630],[565,2429,2430,2431,2487,2488,2574,2575,2633,2634,917,2686,1048,2817,917,2879,3004,3005,1048,3084,3178,3179,3230,3231,3292],{},"Aus den ersten beiden Gleichungen folgt ",[569,2432,2434,2454],{"className":2433},[572],[569,2435,2437],{"className":2436},[576],[578,2438,2439],{"xmlns":580},[582,2440,2441,2451],{},[585,2442,2443,2445,2447,2449],{},[588,2444,605],{},[592,2446,743],{},[745,2448,1787],{},[588,2450,598],{},[610,2452,2453],{"encoding":612},"y = 2x",[569,2455,2457,2475],{"className":2456,"ariaHidden":601},[617],[569,2458,2460,2463,2466,2469,2472],{"className":2459},[621],[569,2461],{"className":2462,"style":863},[625],[569,2464,605],{"className":2465,"style":652},[630,631],[569,2467],{"className":2468,"style":784},[647],[569,2470,743],{"className":2471},[788],[569,2473],{"className":2474,"style":784},[647],[569,2476,2478,2481,2484],{"className":2477},[621],[569,2479],{"className":2480,"style":798},[625],[569,2482,1787],{"className":2483},[630],[569,2485,598],{"className":2486},[630,631],". Eingesetzt: ",[569,2489,2491,2515],{"className":2490},[572],[569,2492,2494],{"className":2493},[576],[578,2495,2496],{"xmlns":580},[582,2497,2498,2512],{},[585,2499,2500,2502,2508,2510],{},[745,2501,1896],{},[1878,2503,2504,2506],{},[588,2505,598],{},[745,2507,1787],{},[592,2509,743],{},[745,2511,1896],{},[610,2513,2514],{"encoding":612},"5x^2 = 5",[569,2516,2518,2565],{"className":2517,"ariaHidden":601},[617],[569,2519,2521,2524,2527,2556,2559,2562],{"className":2520},[621],[569,2522],{"className":2523,"style":1928},[625],[569,2525,1896],{"className":2526},[630],[569,2528,2530,2533],{"className":2529},[630],[569,2531,598],{"className":2532},[630,631],[569,2534,2536],{"className":2535},[1174],[569,2537,2539],{"className":2538},[1178],[569,2540,2542],{"className":2541},[1183],[569,2543,2545],{"className":2544,"style":1928},[1187],[569,2546,2547,2550],{"style":1931},[569,2548],{"className":2549,"style":1196},[1195],[569,2551,2553],{"className":2552},[1200,1201,1202,1203],[569,2554,1787],{"className":2555},[630,1203],[569,2557],{"className":2558,"style":784},[647],[569,2560,743],{"className":2561},[788],[569,2563],{"className":2564,"style":784},[647],[569,2566,2568,2571],{"className":2567},[621],[569,2569],{"className":2570,"style":798},[625],[569,2572,1896],{"className":2573},[630],", also ",[569,2576,2578,2599],{"className":2577},[572],[569,2579,2581],{"className":2580},[576],[578,2582,2583],{"xmlns":580},[582,2584,2585,2596],{},[585,2586,2587,2589,2591,2594],{},[588,2588,598],{},[592,2590,743],{},[592,2592,2593],{},"±",[745,2595,2205],{},[610,2597,2598],{"encoding":612},"x = \\pm 1",[569,2600,2602,2620],{"className":2601,"ariaHidden":601},[617],[569,2603,2605,2608,2611,2614,2617],{"className":2604},[621],[569,2606],{"className":2607,"style":1015},[625],[569,2609,598],{"className":2610},[630,631],[569,2612],{"className":2613,"style":784},[647],[569,2615,743],{"className":2616},[788],[569,2618],{"className":2619,"style":784},[647],[569,2621,2623,2627,2630],{"className":2622},[621],[569,2624],{"className":2625,"style":2626},[625],"height:0.7278em;vertical-align:-0.0833em;",[569,2628,2593],{"className":2629},[630],[569,2631,2205],{"className":2632},[630],". Die Kandidaten sind ",[569,2635,2637,2659],{"className":2636},[572],[569,2638,2640],{"className":2639},[576],[578,2641,2642],{"xmlns":580},[582,2643,2644,2656],{},[585,2645,2646,2648,2650,2652,2654],{},[592,2647,595],{"stretchy":594},[745,2649,2205],{},[592,2651,602],{"separator":601},[745,2653,1787],{},[592,2655,608],{"stretchy":594},[610,2657,2658],{"encoding":612},"(1, 2)",[569,2660,2662],{"className":2661,"ariaHidden":601},[617],[569,2663,2665,2668,2671,2674,2677,2680,2683],{"className":2664},[621],[569,2666],{"className":2667,"style":626},[625],[569,2669,595],{"className":2670},[636],[569,2672,2205],{"className":2673},[630],[569,2675,602],{"className":2676},[643],[569,2678],{"className":2679,"style":648},[647],[569,2681,1787],{"className":2682},[630],[569,2684,608],{"className":2685},[656],[569,2687,2689,2712],{"className":2688},[572],[569,2690,2692],{"className":2691},[576],[578,2693,2694],{"xmlns":580},[582,2695,2696,2709],{},[585,2697,2698,2700,2702],{},[588,2699,900],{},[592,2701,743],{},[2703,2704,2705,2707],"mfrac",{},[745,2706,2205],{},[745,2708,1787],{},[610,2710,2711],{"encoding":612},"\\lambda = \\frac{1}{2}",[569,2713,2715,2733],{"className":2714,"ariaHidden":601},[617],[569,2716,2718,2721,2724,2727,2730],{"className":2717},[621],[569,2719],{"className":2720,"style":913},[625],[569,2722,900],{"className":2723},[630,631],[569,2725],{"className":2726,"style":784},[647],[569,2728,743],{"className":2729},[788],[569,2731],{"className":2732,"style":784},[647],[569,2734,2736,2740],{"className":2735},[621],[569,2737],{"className":2738,"style":2739},[625],"height:1.1901em;vertical-align:-0.345em;",[569,2741,2743,2747,2814],{"className":2742},[630],[569,2744],{"className":2745},[636,2746],"nulldelimiter",[569,2748,2750],{"className":2749},[2703],[569,2751,2753,2805],{"className":2752},[1178,1179],[569,2754,2756,2802],{"className":2755},[1183],[569,2757,2760,2776,2787],{"className":2758,"style":2759},[1187],"height:0.8451em;",[569,2761,2763,2767],{"style":2762},"top:-2.655em;",[569,2764],{"className":2765,"style":2766},[1195],"height:3em;",[569,2768,2770],{"className":2769},[1200,1201,1202,1203],[569,2771,2773],{"className":2772},[630,1203],[569,2774,1787],{"className":2775},[630,1203],[569,2777,2779,2782],{"style":2778},"top:-3.23em;",[569,2780],{"className":2781,"style":2766},[1195],[569,2783],{"className":2784,"style":2786},[2785],"frac-line","border-bottom-width:0.04em;",[569,2788,2790,2793],{"style":2789},"top:-3.394em;",[569,2791],{"className":2792,"style":2766},[1195],[569,2794,2796],{"className":2795},[1200,1201,1202,1203],[569,2797,2799],{"className":2798},[630,1203],[569,2800,2205],{"className":2801},[630,1203],[569,2803,1211],{"className":2804},[1210],[569,2806,2808],{"className":2807},[1183],[569,2809,2812],{"className":2810,"style":2811},[1187],"height:0.345em;",[569,2813],{},[569,2815],{"className":2816},[656,2746],[569,2818,2820,2846],{"className":2819},[572],[569,2821,2823],{"className":2822},[576],[578,2824,2825],{"xmlns":580},[582,2826,2827,2843],{},[585,2828,2829,2831,2833,2835,2837,2839,2841],{},[592,2830,595],{"stretchy":594},[592,2832,1489],{},[745,2834,2205],{},[592,2836,602],{"separator":601},[592,2838,1489],{},[745,2840,1787],{},[592,2842,608],{"stretchy":594},[610,2844,2845],{"encoding":612},"(-1, -2)",[569,2847,2849],{"className":2848,"ariaHidden":601},[617],[569,2850,2852,2855,2858,2861,2864,2867,2870,2873,2876],{"className":2851},[621],[569,2853],{"className":2854,"style":626},[625],[569,2856,595],{"className":2857},[636],[569,2859,1489],{"className":2860},[630],[569,2862,2205],{"className":2863},[630],[569,2865,602],{"className":2866},[643],[569,2868],{"className":2869,"style":648},[647],[569,2871,1489],{"className":2872},[630],[569,2874,1787],{"className":2875},[630],[569,2877,608],{"className":2878},[656],[569,2880,2882,2906],{"className":2881},[572],[569,2883,2885],{"className":2884},[576],[578,2886,2887],{"xmlns":580},[582,2888,2889,2903],{},[585,2890,2891,2893,2895,2897],{},[588,2892,900],{},[592,2894,743],{},[592,2896,1489],{},[2703,2898,2899,2901],{},[745,2900,2205],{},[745,2902,1787],{},[610,2904,2905],{"encoding":612},"\\lambda = -\\frac{1}{2}",[569,2907,2909,2927],{"className":2908,"ariaHidden":601},[617],[569,2910,2912,2915,2918,2921,2924],{"className":2911},[621],[569,2913],{"className":2914,"style":913},[625],[569,2916,900],{"className":2917},[630,631],[569,2919],{"className":2920,"style":784},[647],[569,2922,743],{"className":2923},[788],[569,2925],{"className":2926,"style":784},[647],[569,2928,2930,2933,2936],{"className":2929},[621],[569,2931],{"className":2932,"style":2739},[625],[569,2934,1489],{"className":2935},[630],[569,2937,2939,2942,3001],{"className":2938},[630],[569,2940],{"className":2941},[636,2746],[569,2943,2945],{"className":2944},[2703],[569,2946,2948,2993],{"className":2947},[1178,1179],[569,2949,2951,2990],{"className":2950},[1183],[569,2952,2954,2968,2976],{"className":2953,"style":2759},[1187],[569,2955,2956,2959],{"style":2762},[569,2957],{"className":2958,"style":2766},[1195],[569,2960,2962],{"className":2961},[1200,1201,1202,1203],[569,2963,2965],{"className":2964},[630,1203],[569,2966,1787],{"className":2967},[630,1203],[569,2969,2970,2973],{"style":2778},[569,2971],{"className":2972,"style":2766},[1195],[569,2974],{"className":2975,"style":2786},[2785],[569,2977,2978,2981],{"style":2789},[569,2979],{"className":2980,"style":2766},[1195],[569,2982,2984],{"className":2983},[1200,1201,1202,1203],[569,2985,2987],{"className":2986},[630,1203],[569,2988,2205],{"className":2989},[630,1203],[569,2991,1211],{"className":2992},[1210],[569,2994,2996],{"className":2995},[1183],[569,2997,2999],{"className":2998,"style":2811},[1187],[569,3000],{},[569,3002],{"className":3003},[656,2746],". Wegen ",[569,3006,3008,3036],{"className":3007},[572],[569,3009,3011],{"className":3010},[576],[578,3012,3013],{"xmlns":580},[582,3014,3015,3033],{},[585,3016,3017,3019,3021,3023,3025,3027,3029,3031],{},[588,3018,590],{},[592,3020,595],{"stretchy":594},[745,3022,2205],{},[592,3024,602],{"separator":601},[745,3026,1787],{},[592,3028,608],{"stretchy":594},[592,3030,743],{},[745,3032,1896],{},[610,3034,3035],{"encoding":612},"f(1, 2) = 5",[569,3037,3039,3075],{"className":3038,"ariaHidden":601},[617],[569,3040,3042,3045,3048,3051,3054,3057,3060,3063,3066,3069,3072],{"className":3041},[621],[569,3043],{"className":3044,"style":626},[625],[569,3046,590],{"className":3047,"style":632},[630,631],[569,3049,595],{"className":3050},[636],[569,3052,2205],{"className":3053},[630],[569,3055,602],{"className":3056},[643],[569,3058],{"className":3059,"style":648},[647],[569,3061,1787],{"className":3062},[630],[569,3064,608],{"className":3065},[656],[569,3067],{"className":3068,"style":784},[647],[569,3070,743],{"className":3071},[788],[569,3073],{"className":3074,"style":784},[647],[569,3076,3078,3081],{"className":3077},[621],[569,3079],{"className":3080,"style":798},[625],[569,3082,1896],{"className":3083},[630],[569,3085,3087,3121],{"className":3086},[572],[569,3088,3090],{"className":3089},[576],[578,3091,3092],{"xmlns":580},[582,3093,3094,3118],{},[585,3095,3096,3098,3100,3102,3104,3106,3108,3110,3112,3114,3116],{},[588,3097,590],{},[592,3099,595],{"stretchy":594},[592,3101,1489],{},[745,3103,2205],{},[592,3105,602],{"separator":601},[592,3107,1489],{},[745,3109,1787],{},[592,3111,608],{"stretchy":594},[592,3113,743],{},[592,3115,1489],{},[745,3117,1896],{},[610,3119,3120],{"encoding":612},"f(-1, -2) = -5",[569,3122,3124,3166],{"className":3123,"ariaHidden":601},[617],[569,3125,3127,3130,3133,3136,3139,3142,3145,3148,3151,3154,3157,3160,3163],{"className":3126},[621],[569,3128],{"className":3129,"style":626},[625],[569,3131,590],{"className":3132,"style":632},[630,631],[569,3134,595],{"className":3135},[636],[569,3137,1489],{"className":3138},[630],[569,3140,2205],{"className":3141},[630],[569,3143,602],{"className":3144},[643],[569,3146],{"className":3147,"style":648},[647],[569,3149,1489],{"className":3150},[630],[569,3152,1787],{"className":3153},[630],[569,3155,608],{"className":3156},[656],[569,3158],{"className":3159,"style":784},[647],[569,3161,743],{"className":3162},[788],[569,3164],{"className":3165,"style":784},[647],[569,3167,3169,3172,3175],{"className":3168},[621],[569,3170],{"className":3171,"style":2626},[625],[569,3173,1489],{"className":3174},[630],[569,3176,1896],{"className":3177},[630]," liegt in ",[569,3180,3182,3203],{"className":3181},[572],[569,3183,3185],{"className":3184},[576],[578,3186,3187],{"xmlns":580},[582,3188,3189,3201],{},[585,3190,3191,3193,3195,3197,3199],{},[592,3192,595],{"stretchy":594},[745,3194,2205],{},[592,3196,602],{"separator":601},[745,3198,1787],{},[592,3200,608],{"stretchy":594},[610,3202,2658],{"encoding":612},[569,3204,3206],{"className":3205,"ariaHidden":601},[617],[569,3207,3209,3212,3215,3218,3221,3224,3227],{"className":3208},[621],[569,3210],{"className":3211,"style":626},[625],[569,3213,595],{"className":3214},[636],[569,3216,2205],{"className":3217},[630],[569,3219,602],{"className":3220},[643],[569,3222],{"className":3223,"style":648},[647],[569,3225,1787],{"className":3226},[630],[569,3228,608],{"className":3229},[656]," das Maximum und in ",[569,3232,3234,3259],{"className":3233},[572],[569,3235,3237],{"className":3236},[576],[578,3238,3239],{"xmlns":580},[582,3240,3241,3257],{},[585,3242,3243,3245,3247,3249,3251,3253,3255],{},[592,3244,595],{"stretchy":594},[592,3246,1489],{},[745,3248,2205],{},[592,3250,602],{"separator":601},[592,3252,1489],{},[745,3254,1787],{},[592,3256,608],{"stretchy":594},[610,3258,2845],{"encoding":612},[569,3260,3262],{"className":3261,"ariaHidden":601},[617],[569,3263,3265,3268,3271,3274,3277,3280,3283,3286,3289],{"className":3264},[621],[569,3266],{"className":3267,"style":626},[625],[569,3269,595],{"className":3270},[636],[569,3272,1489],{"className":3273},[630],[569,3275,2205],{"className":3276},[630],[569,3278,602],{"className":3279},[643],[569,3281],{"className":3282,"style":648},[647],[569,3284,1489],{"className":3285},[630],[569,3287,1787],{"className":3288},[630],[569,3290,608],{"className":3291},[656]," das Minimum.",[565,3294,3295,3296,3325,3326,1048,3382,3487,3488,1048,3544,2574,3600,3651,3652,917,3725,3845,3846,986],{},"Welches Rechteck mit Umfang ",[569,3297,3299,3313],{"className":3298},[572],[569,3300,3302],{"className":3301},[576],[578,3303,3304],{"xmlns":580},[582,3305,3306,3311],{},[585,3307,3308],{},[745,3309,3310],{},"20",[610,3312,3310],{"encoding":612},[569,3314,3316],{"className":3315,"ariaHidden":601},[617],[569,3317,3319,3322],{"className":3318},[621],[569,3320],{"className":3321,"style":798},[625],[569,3323,3310],{"className":3324},[630]," hat den größten Flächeninhalt? Mit ",[569,3327,3329,3349],{"className":3328},[572],[569,3330,3332],{"className":3331},[576],[578,3333,3334],{"xmlns":580},[582,3335,3336,3346],{},[585,3337,3338,3340,3342,3344],{},[588,3339,590],{},[592,3341,743],{},[588,3343,598],{},[588,3345,605],{},[610,3347,3348],{"encoding":612},"f = xy",[569,3350,3352,3370],{"className":3351,"ariaHidden":601},[617],[569,3353,3355,3358,3361,3364,3367],{"className":3354},[621],[569,3356],{"className":3357,"style":828},[625],[569,3359,590],{"className":3360,"style":632},[630,631],[569,3362],{"className":3363,"style":784},[647],[569,3365,743],{"className":3366},[788],[569,3368],{"className":3369,"style":784},[647],[569,3371,3373,3376,3379],{"className":3372},[621],[569,3374],{"className":3375,"style":863},[625],[569,3377,598],{"className":3378},[630,631],[569,3380,605],{"className":3381,"style":652},[630,631],[569,3383,3385,3415],{"className":3384},[572],[569,3386,3388],{"className":3387},[576],[578,3389,3390],{"xmlns":580},[582,3391,3392,3412],{},[585,3393,3394,3396,3398,3400,3402,3404,3406,3408,3410],{},[588,3395,730],{},[592,3397,743],{},[745,3399,1787],{},[588,3401,598],{},[592,3403,1784],{},[745,3405,1787],{},[588,3407,605],{},[592,3409,1489],{},[745,3411,3310],{},[610,3413,3414],{"encoding":612},"g = 2x + 2y - 20",[569,3416,3418,3436,3457,3478],{"className":3417,"ariaHidden":601},[617],[569,3419,3421,3424,3427,3430,3433],{"className":3420},[621],[569,3422],{"className":3423,"style":863},[625],[569,3425,730],{"className":3426,"style":652},[630,631],[569,3428],{"className":3429,"style":784},[647],[569,3431,743],{"className":3432},[788],[569,3434],{"className":3435,"style":784},[647],[569,3437,3439,3442,3445,3448,3451,3454],{"className":3438},[621],[569,3440],{"className":3441,"style":2626},[625],[569,3443,1787],{"className":3444},[630],[569,3446,598],{"className":3447},[630,631],[569,3449],{"className":3450,"style":1589},[647],[569,3452,1784],{"className":3453},[1593],[569,3455],{"className":3456,"style":1589},[647],[569,3458,3460,3463,3466,3469,3472,3475],{"className":3459},[621],[569,3461],{"className":3462,"style":1857},[625],[569,3464,1787],{"className":3465},[630],[569,3467,605],{"className":3468,"style":652},[630,631],[569,3470],{"className":3471,"style":1589},[647],[569,3473,1489],{"className":3474},[1593],[569,3476],{"className":3477,"style":1589},[647],[569,3479,3481,3484],{"className":3480},[621],[569,3482],{"className":3483,"style":798},[625],[569,3485,3310],{"className":3486},[630]," gilt ",[569,3489,3491,3511],{"className":3490},[572],[569,3492,3494],{"className":3493},[576],[578,3495,3496],{"xmlns":580},[582,3497,3498,3508],{},[585,3499,3500,3502,3504,3506],{},[588,3501,605],{},[592,3503,743],{},[745,3505,1787],{},[588,3507,900],{},[610,3509,3510],{"encoding":612},"y = 2\\lambda",[569,3512,3514,3532],{"className":3513,"ariaHidden":601},[617],[569,3515,3517,3520,3523,3526,3529],{"className":3516},[621],[569,3518],{"className":3519,"style":863},[625],[569,3521,605],{"className":3522,"style":652},[630,631],[569,3524],{"className":3525,"style":784},[647],[569,3527,743],{"className":3528},[788],[569,3530],{"className":3531,"style":784},[647],[569,3533,3535,3538,3541],{"className":3534},[621],[569,3536],{"className":3537,"style":913},[625],[569,3539,1787],{"className":3540},[630],[569,3542,900],{"className":3543},[630,631],[569,3545,3547,3567],{"className":3546},[572],[569,3548,3550],{"className":3549},[576],[578,3551,3552],{"xmlns":580},[582,3553,3554,3564],{},[585,3555,3556,3558,3560,3562],{},[588,3557,598],{},[592,3559,743],{},[745,3561,1787],{},[588,3563,900],{},[610,3565,3566],{"encoding":612},"x = 2\\lambda",[569,3568,3570,3588],{"className":3569,"ariaHidden":601},[617],[569,3571,3573,3576,3579,3582,3585],{"className":3572},[621],[569,3574],{"className":3575,"style":1015},[625],[569,3577,598],{"className":3578},[630,631],[569,3580],{"className":3581,"style":784},[647],[569,3583,743],{"className":3584},[788],[569,3586],{"className":3587,"style":784},[647],[569,3589,3591,3594,3597],{"className":3590},[621],[569,3592],{"className":3593,"style":913},[625],[569,3595,1787],{"className":3596},[630],[569,3598,900],{"className":3599},[630,631],[569,3601,3603,3621],{"className":3602},[572],[569,3604,3606],{"className":3605},[576],[578,3607,3608],{"xmlns":580},[582,3609,3610,3618],{},[585,3611,3612,3614,3616],{},[588,3613,598],{},[592,3615,743],{},[588,3617,605],{},[610,3619,3620],{"encoding":612},"x = y",[569,3622,3624,3642],{"className":3623,"ariaHidden":601},[617],[569,3625,3627,3630,3633,3636,3639],{"className":3626},[621],[569,3628],{"className":3629,"style":1015},[625],[569,3631,598],{"className":3632},[630,631],[569,3634],{"className":3635,"style":784},[647],[569,3637,743],{"className":3638},[788],[569,3640],{"className":3641,"style":784},[647],[569,3643,3645,3648],{"className":3644},[621],[569,3646],{"className":3647,"style":863},[625],[569,3649,605],{"className":3650,"style":652},[630,631],". Aus der Nebenbedingung folgt ",[569,3653,3655,3677],{"className":3654},[572],[569,3656,3658],{"className":3657},[576],[578,3659,3660],{"xmlns":580},[582,3661,3662,3674],{},[585,3663,3664,3666,3668,3670,3672],{},[588,3665,598],{},[592,3667,743],{},[588,3669,605],{},[592,3671,743],{},[745,3673,1896],{},[610,3675,3676],{"encoding":612},"x = y = 5",[569,3678,3680,3698,3716],{"className":3679,"ariaHidden":601},[617],[569,3681,3683,3686,3689,3692,3695],{"className":3682},[621],[569,3684],{"className":3685,"style":1015},[625],[569,3687,598],{"className":3688},[630,631],[569,3690],{"className":3691,"style":784},[647],[569,3693,743],{"className":3694},[788],[569,3696],{"className":3697,"style":784},[647],[569,3699,3701,3704,3707,3710,3713],{"className":3700},[621],[569,3702],{"className":3703,"style":863},[625],[569,3705,605],{"className":3706,"style":652},[630,631],[569,3708],{"className":3709,"style":784},[647],[569,3711,743],{"className":3712},[788],[569,3714],{"className":3715,"style":784},[647],[569,3717,3719,3722],{"className":3718},[621],[569,3720],{"className":3721,"style":798},[625],[569,3723,1896],{"className":3724},[630],[569,3726,3728,3750],{"className":3727},[572],[569,3729,3731],{"className":3730},[576],[578,3732,3733],{"xmlns":580},[582,3734,3735,3747],{},[585,3736,3737,3739,3741],{},[588,3738,900],{},[592,3740,743],{},[2703,3742,3743,3745],{},[745,3744,1896],{},[745,3746,1787],{},[610,3748,3749],{"encoding":612},"\\lambda = \\frac{5}{2}",[569,3751,3753,3771],{"className":3752,"ariaHidden":601},[617],[569,3754,3756,3759,3762,3765,3768],{"className":3755},[621],[569,3757],{"className":3758,"style":913},[625],[569,3760,900],{"className":3761},[630,631],[569,3763],{"className":3764,"style":784},[647],[569,3766,743],{"className":3767},[788],[569,3769],{"className":3770,"style":784},[647],[569,3772,3774,3777],{"className":3773},[621],[569,3775],{"className":3776,"style":2739},[625],[569,3778,3780,3783,3842],{"className":3779},[630],[569,3781],{"className":3782},[636,2746],[569,3784,3786],{"className":3785},[2703],[569,3787,3789,3834],{"className":3788},[1178,1179],[569,3790,3792,3831],{"className":3791},[1183],[569,3793,3795,3809,3817],{"className":3794,"style":2759},[1187],[569,3796,3797,3800],{"style":2762},[569,3798],{"className":3799,"style":2766},[1195],[569,3801,3803],{"className":3802},[1200,1201,1202,1203],[569,3804,3806],{"className":3805},[630,1203],[569,3807,1787],{"className":3808},[630,1203],[569,3810,3811,3814],{"style":2778},[569,3812],{"className":3813,"style":2766},[1195],[569,3815],{"className":3816,"style":2786},[2785],[569,3818,3819,3822],{"style":2789},[569,3820],{"className":3821,"style":2766},[1195],[569,3823,3825],{"className":3824},[1200,1201,1202,1203],[569,3826,3828],{"className":3827},[630,1203],[569,3829,1896],{"className":3830},[630,1203],[569,3832,1211],{"className":3833},[1210],[569,3835,3837],{"className":3836},[1183],[569,3838,3840],{"className":3839,"style":2811},[1187],[569,3841],{},[569,3843],{"className":3844},[656,2746]," und dem Flächeninhalt ",[569,3847,3849,3863],{"className":3848},[572],[569,3850,3852],{"className":3851},[576],[578,3853,3854],{"xmlns":580},[582,3855,3856,3861],{},[585,3857,3858],{},[745,3859,3860],{},"25",[610,3862,3860],{"encoding":612},[569,3864,3866],{"className":3865,"ariaHidden":601},[617],[569,3867,3869,3872],{"className":3868},[621],[569,3870],{"className":3871,"style":798},[625],[569,3873,3860],{"className":3874},[630],[560,3876,3878],{"id":3877},"typische-fehler","Typische Fehler",[3880,3881,3882,3937,3940,4056],"ul",{},[3883,3884,3885,3886,3936],"li",{},"Die Nebenbedingung ",[569,3887,3889,3906],{"className":3888},[572],[569,3890,3892],{"className":3891},[576],[578,3893,3894],{"xmlns":580},[582,3895,3896,3904],{},[585,3897,3898,3900,3902],{},[588,3899,730],{},[592,3901,743],{},[745,3903,747],{},[610,3905,853],{"encoding":612},[569,3907,3909,3927],{"className":3908,"ariaHidden":601},[617],[569,3910,3912,3915,3918,3921,3924],{"className":3911},[621],[569,3913],{"className":3914,"style":863},[625],[569,3916,730],{"className":3917,"style":652},[630,631],[569,3919],{"className":3920,"style":784},[647],[569,3922,743],{"className":3923},[788],[569,3925],{"className":3926,"style":784},[647],[569,3928,3930,3933],{"className":3929},[621],[569,3931],{"className":3932,"style":798},[625],[569,3934,747],{"className":3935},[630]," nicht ins Gleichungssystem aufnehmen. Ohne sie ist das System unterbestimmt.",[3883,3938,3939],{},"Jeden Kandidaten für ein Extremum halten. Die Methode liefert nur notwendige Bedingungen; man vergleicht die Funktionswerte oder argumentiert anders.",[3883,3941,3942,3943,4055],{},"Punkte mit ",[569,3944,3946,3972],{"className":3945},[572],[569,3947,3949],{"className":3948},[576],[578,3950,3951],{"xmlns":580},[582,3952,3953,3969],{},[585,3954,3955,3957,3959,3961],{},[588,3956,933],{"mathvariant":932},[588,3958,730],{},[592,3960,743],{},[3962,3963,3964,3966],"mover",{"accent":601},[745,3965,747],{},[592,3967,3968],{},"⃗",[610,3970,3971],{"encoding":612},"\\nabla g = \\vec 0",[569,3973,3975,3997],{"className":3974,"ariaHidden":601},[617],[569,3976,3978,3982,3985,3988,3991,3994],{"className":3977},[621],[569,3979],{"className":3980,"style":3981},[625],"height:0.8778em;vertical-align:-0.1944em;",[569,3983,933],{"className":3984},[630],[569,3986,730],{"className":3987,"style":652},[630,631],[569,3989],{"className":3990,"style":784},[647],[569,3992,743],{"className":3993},[788],[569,3995],{"className":3996,"style":784},[647],[569,3998,4000,4004],{"className":3999},[621],[569,4001],{"className":4002,"style":4003},[625],"height:0.9274em;",[569,4005,4008],{"className":4006},[630,4007],"accent",[569,4009,4011],{"className":4010},[1178],[569,4012,4014],{"className":4013},[1183],[569,4015,4017,4026],{"className":4016,"style":4003},[1187],[569,4018,4020,4023],{"style":4019},"top:-3em;",[569,4021],{"className":4022,"style":2766},[1195],[569,4024,747],{"className":4025},[630],[569,4027,4029,4032],{"style":4028},"top:-3.2134em;",[569,4030],{"className":4031,"style":2766},[1195],[569,4033,4037],{"className":4034,"style":4036},[4035],"accent-body","left:-0.2355em;",[569,4038,4042],{"className":4039,"style":4041},[4040],"overlay","height:0.714em;width:0.471em;",[4043,4044,4051],"svg",{"xmlns":4045,"width":4046,"height":4047,"style":4048,"viewBox":4049,"preserveAspectRatio":4050},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","0.471em","0.714em","width:0.471em","0 0 471 714","xMinYMin",[4052,4053],"path",{"d":4054},"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z"," übersehen. Dort greift die Methode nicht, sie müssen separat untersucht werden.",[3883,4057,4058,4059,4087],{},"Beim Auflösen durch ",[569,4060,4062,4075],{"className":4061},[572],[569,4063,4065],{"className":4064},[576],[578,4066,4067],{"xmlns":580},[582,4068,4069,4073],{},[585,4070,4071],{},[588,4072,900],{},[610,4074,903],{"encoding":612},[569,4076,4078],{"className":4077,"ariaHidden":601},[617],[569,4079,4081,4084],{"className":4080},[621],[569,4082],{"className":4083,"style":913},[625],[569,4085,900],{"className":4086},[630,631]," oder eine Variable teilen, die null sein kann, und so Lösungen verlieren.",{"title":4089,"searchDepth":4090,"depth":4090,"links":4091},"",2,[4092,4093,4094],{"id":562,"depth":4090,"text":563},{"id":1750,"depth":4090,"text":1751},{"id":3877,"depth":4090,"text":3878},[4096,4098,4100,4102,4104,4106,4108,4111,4113,4115,4117],{"lhs":4097,"rhs":747},"1 - 2*(1\u002F2)*1",{"lhs":4099,"rhs":747},"2 - 2*(1\u002F2)*2",{"lhs":4101,"rhs":747},"1^2 + 2^2 - 5",{"lhs":4103,"rhs":747},"1 - 2*(-1\u002F2)*(-1)",{"lhs":4105,"rhs":747},"2 - 2*(-1\u002F2)*(-2)",{"lhs":4107,"rhs":1896},"1 + 2*2",{"lhs":4109,"rhs":4110},"-1 + 2*(-2)","-5",{"lhs":4112,"rhs":1896},"round(max(map(0:3599, f(k) = sqrt(5)*cos(k*pi\u002F1800) + 2*sqrt(5)*sin(k*pi\u002F1800))), 4)",{"lhs":4114,"rhs":747},"5 - (5\u002F2)*2",{"lhs":4116,"rhs":747},"2*5 + 2*5 - 20",{"lhs":4118,"rhs":3860},"5*5","f, g \\text{ stetig differenzierbar},\\ \\nabla g(x_0, y_0) \\neq \\vec{0}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>g\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f, g\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>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">g\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">stetig\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>\u003Cmi mathvariant=\"normal\">∇\u003C\u002Fmi>\u003Cmi>g\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>y\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmn>0\u003C\u002Fmn>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\nabla g(x_0, y_0) \\neq \\vec{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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∇\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">g\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=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\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:-0.0359em;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\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace 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