设 $f(x, y)$ 在点 $P_0\left(x_0, y_0\right)$ 处有二阶连续偏导数, 且 $f(x, y)$ 在 $P_0$ 处取得极大 值, 则
$\text{A.}$ $f_{x x}^{\prime \prime}\left(P_0\right) \geqslant 0, f_{y y}^{\prime \prime}\left(P_0\right) \geqslant 0$.
$\text{B.}$ $f_{x x}^{\prime \prime}\left(P_0\right) < 0, f_{y y}^{\prime \prime}\left(P_0\right) < 0$.
$\text{C.}$ $f_{x x}^{\prime \prime}\left(P_0\right) \leqslant 0, f_{y y}^{\prime \prime}\left(P_0\right) \leqslant 0$.
$\text{D.}$ $f_{x x}^{\prime \prime}\left(P_0\right) \leqslant 0, f_{y y}^{\prime \prime}\left(P_0\right) \geqslant 0$.