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受欢迎的函数 >

extreme f(x,y)=(x^2-8x)(y^2-3y)

解答

极值点

f (x, y) = (x^{2} - 8 x) (y^{2} - 3 y)

解答

鞍点 (0, 3), 鞍点 (8, 3), 鞍点 (0, 0), 鞍点 (8, 0), 极大值 (4, \frac{3}{2})

求解步骤

找到临界点:

(0, 3), (8, 3), (0, 0), (8, 0), (4, \frac{3}{2})

\frac{\partial ^{2} f}{\partial x ^{2}} = 2 (x^{2} - 8 x)

D (x, y) = - 12 x^{2} y^{2} + 36 x^{2} y - 36 x^{2} + 96 x y^{2} - 288 x y + 288 x - 256 y^{2} + 768 y - 576

检查在每个临界点处的符号

检查临界点

(0, 3) :

鞍点

检查临界点

(8, 3) :

鞍点

检查临界点

(0, 0) :

鞍点

检查临界点

(8, 0) :

鞍点

检查临界点

(4, \frac{3}{2}) :

极大值

鞍点 (0, 3), 鞍点 (8, 3), 鞍点 (0, 0), 鞍点 (8, 0), 极大值 (4, \frac{3}{2})

作图

流行的例子

extreme F(x)=(5x^2)/(x^2-16)

e x t re m e F (x) = \frac{5 x ^{2}}{x ^{2} - 16}

extreme f(x)=(In(x^2-1))/(x^2-1)

e x t re m e f (x) = \frac{I n ( x ^{2} - 1 )}{x ^{2} - 1}

extreme 16(-1/(x^2)-2/(x^3))

e x t re m e 16 (- \frac{1}{x ^{2}} - \frac{2}{x ^{3}})

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e x t re m e f (x, y) = x^{2} + x y + y^{2} - 22 y + 161

extreme f(x)=3x^6-7x^5

e x t re m e f (x) = 3 x^{6} - 7 x^{5}