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受欢迎的函数 >

extreme f(x,y)=x^2+4y^2-2ln(xy)

解答

极值点

f (x, y) = x^{2} + 4 y^{2} - 2 ln (x y)

解答

极小值 (1, \frac{1}{2}), 极小值 (- 1, \frac{1}{2}), 极小值 (1, - \frac{1}{2}), 极小值 (- 1, - \frac{1}{2})

求解步骤

找到临界点:

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

\frac{\partial ^{2} f}{\partial x ^{2}} = 8 + \frac{2}{y ^{2}}

D (x, y) = (\frac{2}{x ^{2}} + 2) (\frac{2}{y ^{2}} + 8)

检查在每个临界点处的符号

检查临界点

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

极小值

检查临界点

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

极小值

检查临界点

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

极小值

检查临界点

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

极小值

极小值 (1, \frac{1}{2}), 极小值 (- 1, \frac{1}{2}), 极小值 (1, - \frac{1}{2}), 极小值 (- 1, - \frac{1}{2})

作图

流行的例子

extreme f(x)=-x^3+2x^2+1,-1<= x<= 1

e x t re m e f (x) = - x^{3} + 2 x^{2} + 1, - 1 \leq x \leq 1

extreme f(x)= 1/4 x^2+x^3-2

e x t re m e f (x) = \frac{1}{4} x^{2} + x^{3} - 2

extreme f(x)=x^3-x^2-x+3

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

extreme f(x,y)=3x^4+3y^4-2xy

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

extreme f(x)=4x^5-60x^3

e x t re m e f (x) = 4 x^{5} - 60 x^{3}