极值存在的必要条件(B013)

问题

设 $z=f(x, y)$ 在点 $\left(x_{0}, y_{0}\right)$ 的一阶偏导数存在, 且 $\left(x_{0}, y_{0}\right)$ 是 $z=$ $f(x, y)$ 的极值点, 则可以推出以下哪个选项所示的结论?

选项

[A].   $\left.\frac{\partial z}{\partial x}\right|_{\left(x, y\right)}$ $=$ $0$, $\left.\frac{\partial z}{\partial y}\right|_{\left(x, y \right)}$ $=$ $0$

[B].   $\left.\frac{\partial z}{\partial x}\right|_{\left(x_{0}, y_{0}\right)}$ $\neq$ $\left.\frac{\partial z}{\partial y}\right|_{\left(x_{0}, y_{0}\right)}$

[C].   $\left.\frac{\partial z}{\partial x}\right|_{\left(x_{0}, y_{0}\right)}$ $=$ $1$, $\left.\frac{\partial z}{\partial y}\right|_{\left(x_{0}, y_{0}\right)}$ $=$ $1$

[D].   $\left.\frac{\partial z}{\partial x}\right|_{\left(x_{0}, y_{0}\right)}$ $=$ $0$, $\left.\frac{\partial z}{\partial y}\right|_{\left(x_{0}, y_{0}\right)}$ $=$ $0$


上一题 - 荒原之梦   答 案   下一题 - 荒原之梦

$\left.\frac{\partial z}{\partial x}\right|_{\left(x_{0}, y_{0}\right)}$ $=$ $0$, $\left.\frac{\partial z}{\partial y}\right|_{\left(x_{0}, y_{0}\right)}$ $=$ $0$


荒原之梦网全部内容均为原创,提供了涵盖考研数学基础知识、考研数学真题、考研数学练习题和计算机科学等方面,大量精心研发的学习资源。

豫 ICP 备 17023611 号-1 | 公网安备 - 荒原之梦 豫公网安备 41142502000132 号 | SiteMap
Copyright © 2017-2024 ZhaoKaifeng.com 版权所有 All Rights Reserved.

Copyright © 2024   zhaokaifeng.com   All Rights Reserved.
豫ICP备17023611号-1
 豫公网安备41142502000132号

荒原之梦 自豪地采用WordPress