extreme f(x,y)=x*e^{x+y^2}

解答

极值点

f (x, y) = x \cdot e^{x + y^{2}}

鞍点 (- 1, 0)

求解步骤

找到临界点:

(- 1, 0)

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

D (x, y) = 4 e^{2 x + 2 y^{2}} x^{2} y^{2} - 4 e^{2 (x + y^{2})} x^{2} y^{2} + 2 e^{2 x + 2 y^{2}} x^{2} + 4 e^{2 x + 2 y^{2}} x - 4 e^{2 (x + y^{2})} y^{2}

检查在每个临界点处的符号

检查临界点

(- 1, 0) :

鞍点

鞍点 (- 1, 0)

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

e x t re m e f (x) = 5 + 6 x - 8 x^{3}

e x t re m e f (x) = 2 x^{3} + 24 x + 5

e x t re m e f (x, y) = 3 - x^{4} + 2 x^{2} - y^{2}

e x t re m e f (x, y) = x y + y x