extreme f(x)=e^{xy}

解答

极值点

f (x) = e^{x y}

鞍点 (0, 0)

求解步骤

找到临界点:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = e^{x y} x^{2}

D (x, y) = - 2 e^{2 x y} x y - e^{2 x y}

检查在每个临界点处的符号

检查临界点

(0, 0) :

鞍点

鞍点 (0, 0)

e x t re m e f (x, y) = 2 x^{4} + 5 x y^{2} + y + 2

e x t re m e f (x, y) = y^{2} + x y + 3 y + 2 x + 3

e x t re m e ln (x - y) + x^{2} + y

e x t re m e f (x) = x^{101} + x^{51} + x + 1

e x t re m e f (x, y) = x^{2} y - 3 x y^{2}