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