extreme f(x,y)=-x^2+5y^2+10x-10y-28

解答

极值点

f (x, y) = - x^{2} + 5 y^{2} + 10 x - 10 y - 28

鞍点 (5, 1)

求解步骤

找到临界点:

(5, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 10

D (x, y) = - 20

检查在每个临界点处的符号

检查临界点

(5, 1) :

鞍点

鞍点 (5, 1)

e x t re m e f (x) = x - 4 x

e x t re m e f (x) = x^{2} + \frac{360}{x}, [0, \infty]

e x t re m e f (x) = x^{2} y + x y^{2}

e x t re m e f (x) = x^{2} - 6 x + 11

e x t re m e f (x) = x + \frac{256}{x ^{2}}