extreme P(x,y)=0.3x^2+0.2y^2+0.1xy-14x-10y+2000

解答

极值点

P (x, y) = 0.3 x^{2} + 0.2 y^{2} + 0.1 x y - 14 x - 10 y + 2000

极小值 (20, 20)

求解步骤

找到临界点:

(20, 20)

\frac{\partial ^{2} f}{\partial x ^{2}} = 0.4

D (x, y) = 0.23

检查在每个临界点处的符号

检查临界点

(20, 20) :

极小值

极小值 (20, 20)

e x t re m e f (x) = x^{2} - 11 x + 24

e x t re m e \frac{x ^{3} + 1}{x}

e x t re m e x^{3} - 2 x^{2} - 4 x + 2

e x t re m e y = ln (x^{2}) + 8 x + 24

e x t re m e f (x) = x^{3} - 2 x^{2} - 4 x + 8, - 1 \leq x \leq 0