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受欢迎的函数 >

extreme f(x,y)=ye^{x^2-y^2}

解答

极值点

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

解答

鞍点 (0, - \frac{1}{2}), 鞍点 (0, \frac{1}{2}), 鞍点 (0, - \frac{1}{2}), 鞍点 (0, \frac{1}{2})

求解步骤

找到临界点:

(0, - \frac{1}{2}), (0, \frac{1}{2}), (0, - \frac{1}{2}), (0, \frac{1}{2})

\frac{\partial ^{2} f}{\partial x ^{2}} = 4 e^{(x + y) (x - y)} y^{3} - 6 e^{(x + y) (x - y)} y

D (x, y) = 16 e^{2 x^{2} - 2 y^{2}} x^{2} y^{4} - 16 e^{2 (x^{2} - y^{2})} x^{2} y^{4} + 8 e^{2 x^{2} - 2 y^{2}} y^{4} - 8 e^{2 x^{2} - 2 y^{2}} x^{2} y^{2} - 12 e^{2 x^{2} - 2 y^{2}} y^{2} - 4 e^{2 (x^{2} - y^{2})} x^{2}

检查在每个临界点处的符号

检查临界点

(0, - \frac{1}{2}) :

鞍点

检查临界点

(0, \frac{1}{2}) :

鞍点

检查临界点

(0, - \frac{1}{2}) :

鞍点

检查临界点

(0, \frac{1}{2}) :

鞍点

鞍点 (0, - \frac{1}{2}), 鞍点 (0, \frac{1}{2}), 鞍点 (0, - \frac{1}{2}), 鞍点 (0, \frac{1}{2})

作图

流行的例子

extreme f(x)=(e^x)/(x^3)

e x t re m e f (x) = \frac{e ^{x}}{x ^{3}}

extreme f(x)=((x^2-8))/(x-3)

e x t re m e f (x) = \frac{( x ^{2} - 8 )}{x - 3}

extreme q(x,y)=x^2-xy+5y^2

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

extreme f(x,y)=6-x^2-4x-y^2

e x t re m e f (x, y) = 6 - x^{2} - 4 x - y^{2}

extreme f(x)=5x^3-4

e x t re m e f (x) = 5 x^{3} - 4