题目

设二元函数 z = f(x, y) 在点 (x_0, y_0) 的某邻域内连续且具有一阶及二阶连续偏导数, 又 f_x(x_0, y_0)= 0、f_y(x_0, y_0)= 0, 令 A = f_(xx)(x_0, y_0), B = f_(xy)(x_0, y_0), C = f_(yy)(x_0, y_0), 则该函数在 (x_0, y_0) 处取得极大值的充分条件是()A. AC - B^2 > 0, A > 0B. AC - B^2 0C. AC - B^2 > 0, A D. AC - B^2

设二元函数 $z = f(x, y)$ 在点 $(x_0, y_0)$ 的某邻域内连续且具有一阶及二阶连续偏导数, 又 $f_x(x_0, y_0)= 0$、$f_y(x_0, y_0)= 0$, 令 $A = f_{xx}(x_0, y_0)$, $B = f_{xy}(x_0, y_0)$, $C = f_{yy}(x_0, y_0)$, 则该函数在 $(x_0, y_0)$ 处取得极大值的充分条件是()

A. $AC - B^2 > 0, A > 0$

B. $AC - B^2 < 0, A > 0$

C. $AC - B^2 > 0, A < 0$

D. $AC - B^2 < 0, A < 0$

题目解答

答案

C. $AC - B^2 > 0, A < 0$