设二元函数 $z=f(x, y)$ 在点 $\left(x_0, y_0\right)$ 的某领域内存在连续的二阶偏导数 $f_x^{\prime} 、 f_{x y}^{\prime \prime} 、 f_{y y}^{\prime \prime}$,且点 $\left(x_0, y_0\right)$ 是驻点, 当 $f_{x y}^{\prime 2}\left(x_0, y_0\right) < f_{y y}^{\prime \prime}\left(x_0, y_0\right) f_{xx}^{\prime \prime}\left(x_0, y_0\right)$, 且 $f_{y y}^{\prime}\left(x_0, y_0\right) < 0$ 时,下列结论正确的是
A
$f\left(x_0, y_0\right)$ 不是极值
B
$f\left(x_0, y_0\right)$ 是极小值
C
$f\left(x_0, y_0\right)$ 是极大值
D
不能判断 $f\left(x_0, y_0\right)$ 是否为极值
E
F