求高数高手解释

2025-05-09 07:57:36
推荐回答(1个)
回答1:

f(x, y) = x^3 + y^3 - 9xy + 27
f' = 3x^2 - 9y, f' = 3y^2 - 9x
联立解 x^2 = 3y, y^2 = 3x 得驻点 O(0, 0), P(3, 3),
f'' = 6x , f'' = -9, f'' = 6y
对于驻点 O(0, 0), A = 0, B = -9, C = 0, AC - B^2 < 0, 不是极值点;
对于驻点 P(3, 3), A = 18 > 0, B = -9, C = 18, AC - B^2 > 0,
是极小值点。极小值 f(3, 3) = 0