设函数 [tex=12.571x2.357]OHpHlp08spOzUuoW7DEI8UQGU5oI0ymbpfLTaAsQGVreaSPi+43aPyPx6TTq0MR0BO0kwCd0ZA/DFao4/+UdUA==[/tex][br][/br]求[tex=2.786x1.357]g1Wo3ALRzTk0js5m9GO2sA==[/tex]的极值,并证明函数[tex=2.786x1.357]g1Wo3ALRzTk0js5m9GO2sA==[/tex]在点[tex=2.286x1.357]sVCzP1QNUT517zJi7AAZqw==[/tex] 处不取极值.[br][/br][br][/br]

2022-06-16

设函数 [tex=12.571x2.357]OHpHlp08spOzUuoW7DEI8UQGU5oI0ymbpfLTaAsQGVreaSPi+43aPyPx6TTq0MR0BO0kwCd0ZA/DFao4/+UdUA==[/tex][br][/br]求[tex=2.786x1.357]g1Wo3ALRzTk0js5m9GO2sA==[/tex]的极值,并证明函数[tex=2.786x1.357]g1Wo3ALRzTk0js5m9GO2sA==[/tex]在点[tex=2.286x1.357]sVCzP1QNUT517zJi7AAZqw==[/tex] 处不取极值.[br][/br][br][/br]

答案：

解 令 [tex=21.714x3.5]7EJHVCtO2IWq3KpdB+jQsudUsLVg42HJbHAV68rndhmObtzqizE7tkqe4x2p1HU9HO8xxDm3sDS0/OJneKJY4kyWXRtrwCSBsaJfrYks8yCUpfiFjQymjn0FLUIMAEiu7VxZjlW9+LP+15Kli76fZivbYaZaUdqzHM1FtVInqPgAZdB/664UFTTxK7UxHmeaQeycM3QJJN5Infqeykp5gj+8mtpnikemoqj67gxntBZ1dQuBta+GOkUBpf1aUdRB[/tex]可得 [tex=5.786x1.357]a6gyOw+JXXZY+qbqlElSY5CxBNefs9WcfAsFQuVmjj0=[/tex] 又[tex=15.214x1.5]tK2jv+ZichfaiDZDwtxQCJKymOYZ6gN7TPR5MEEVd+7s8ivFJk9j8UxYH/wNSQ+3HQnwa/FBLwaaJm1WNFM2xA==[/tex]在 [tex=2.857x1.357]S5YNK18OZZCNnnq5JQ1U0g==[/tex] 处,[tex=5.571x1.429]t1OXcjC8HQVZHU+/C2MdfA==[/tex]且[tex=5.571x1.429]t1OXcjC8HQVZHU+/C2MdfA==[/tex] 所以[tex=2.857x1.357]S5YNK18OZZCNnnq5JQ1U0g==[/tex]为极小值点,且 [tex=6.786x2.357]MykyXH38pVoG5wHQDxq285nRbJ4vyqVdlToUXtfzp7Y=[/tex][tex=4.143x1.357]W1/ZlblUkOzyyc8vhPJz+5XZWPTy/dMw4Mb4vvdcb/4=[/tex]而[tex=17.571x5.214]fnpmC2J6JmQBLyo5NmGAz603V05MZe4Vj6nBrndn08Qnew7897Mkac1KHcz9jsthAJTNKBZsMtZ5LQ3dXfz7lrJrR0kgKPayGKnPy1FlskgybzBLPWyrA+uSZja5HcMLtrdZGgJwrAJbOz5DlG9YgrAW6rvMbSkDqHkxEE5R+F0GN/M84QjnU+bEWL9Y2jXAeDdwpVEwMD9YMxxQsGrIeHRBSzEgZAt+Q/MBGtWbXFRsYkP/YVHs//9apG8KReMMSC9mbRUbMJoZLicHrGVbGw==[/tex]所以[tex=2.786x1.357]g1Wo3ALRzTk0js5m9GO2sA==[/tex] 在[tex=2.286x1.357]sVCzP1QNUT517zJi7AAZqw==[/tex]处不取极值.

举一反三

内容

0
设二维离散随机变量[tex=2.5x1.357]PWg5V4GQQafckGNgbx6gmw==[/tex]的可能值为(0, 0)，(−1, 1)，(−1, 2)，(1, 0)，且取这些值的概率依次为1/6, 1/3, 1/12, 5/12，试求[tex=0.857x1.0]N7iCrOsS+NNEUUlnsYCi1g==[/tex]与[tex=0.643x1.0]O+viFNA0oHTwnBtQyi80Zw==[/tex] 各自的边际分布列．
1
【单选题】Which of the following matrices does not have the same determinant of matrix B: [1, 3, 0, 2; -2, -5, 7, 4; 3, 5, 2, 1; -1, 0, -9,-5] A. [1, 3, 0, 2; -2, -5, 7, 4; 0, 0, 0, 0; -1, 0, -9, -5] B. [1, 3, 0, 2; -2, -5, 7, 4; 1, 0, 9, 5; -1, 0, -9, -5] C. [1, 3, 0, 2; -2, -5, 7, 4; 3, 5, 2, 1; -3, -5, -2, -1] D. [1, 3, 0, 2; -2, -5, 7, 4; 0, 0, 0, 1; -1, 0, -9, -5]
2
以下数组定义中,错误的是( )。 A: int<br/>x[2][3] ={1, 2, 3, 4, 5, 6} ; B: int<br/>x[][3] ={0} ; C: int<br/>x[][3] ={{1, 2, 3} , {4, 5, 6} } ; D: int<br/>x[2][3] ={{1, 2} , {3, 4} , {5, 6} } ;
3
设 [tex=14.929x4.5]5Cmgwu1OybHBcWwAUtmUQdgTeSTqBtCKnqbhBHzdyU5ZII/vU8PieqG16YbUAI+XPtMcNmWugkrmRJv9zxPlbSYXlRT9y3qEId/G95ZpKOyczPcKNZ/S84fcMuaTAa6maW5kIJOr7SFkjj2Pv1IEc12jpVJFO+2/nmYQ5KXgPIA=[/tex] 证明: (1) [tex=2.643x1.357]g1Wo3ALRzTk0js5m9GO2sA==[/tex] 在点 [tex=2.286x1.357]sVCzP1QNUT517zJi7AAZqw==[/tex] 处不连续; (2) 偏导数存在; (3)不可微分.
4
>>>x= [10, 6, 0, 1, 7, 4, 3, 2, 8, 5, 9]>>>print(x.sort()) 语句运行结果正确的是( )。 A: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] B: [10, 6, 0, 1, 7, 4, 3, 2, 8, 5, 9] C: [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0] D: ['2', '4', '0', '6', '10', '7', '8', '3', '9', '1', '5']