zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的函数 >

extreme f(x)=x^2(4-x)^2

解答

极值点

f (x) = x^{2} (4 - x)^{2}

解答

极小值 (0, 0), 极大值 (2, 16), 极小值 (4, 0)

求解步骤

f^{'} (x) = 4 x (x - 4) (x - 2)

Find intervals:

递减

: - \infty < x < 0,

递增

: 0 < x < 2,

递减

: 2 < x < 4,

递增

: 4 < x < \infty

将

x = 0

代入

x^{2} (4 - x)^{2} : 0

极小值 (0, 0)

将

x = 2

代入

x^{2} (4 - x)^{2} : 16

极大值 (2, 16)

将

x = 4

代入

x^{2} (4 - x)^{2} : 0

极小值 (4, 0)

极小值 (0, 0), 极大值 (2, 16), 极小值 (4, 0)

作图

流行的例子

extreme f(x,y)=50+2x+3y-3x^2-y^2-0.5xy

e x t re m e f (x, y) = 50 + 2 x + 3 y - 3 x^{2} - y^{2} - 0.5 x y

extreme U(x,y)=-x^2-3y^2+2xy+100x

e x t re m e U (x, y) = - x^{2} - 3 y^{2} + 2 x y + 100 x

extreme f(x)=x^2+(120)/x

e x t re m e f (x) = x^{2} + \frac{120}{x}

extreme f(x,y)= 1/2 y^4-4xy+2x^4

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

extreme f(x)=2x^5ln(x)

e x t re m e f (x) = 2 x^{5} ln (x)