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^{4/5}(x-5)^2

解答

极值点

f (x) = x^{\frac{4}{5}} (x - 5)^{2}

解答

极小值 (0, 0), 极大值 (\frac{10}{7}, \frac{625 \cdot 1 0 ^{\frac{4}{5}}}{49 \cdot 7 ^{\frac{4}{5}}}), 极小值 (5, 0)

求解步骤

f^{'} (x) = \frac{2 ( 7 x - 10 ) ( - 5 + x )}{5 x ^{\frac{1}{5}}}

Find intervals:

递减

: - \infty < x < 0,

递增

: 0 < x < \frac{10}{7},

递减

: \frac{10}{7} < x < 5,

递增

: 5 < x < \infty

将

x = 0

代入

x^{\frac{4}{5}} (x - 5)^{2} : 0

极小值 (0, 0)

将

x = \frac{10}{7}

代入

x^{\frac{4}{5}} (x - 5)^{2} : \frac{625 \cdot 1 0 ^{\frac{4}{5}}}{49 \cdot 7 ^{\frac{4}{5}}}

极大值 (\frac{10}{7}, \frac{625 \cdot 1 0 ^{\frac{4}{5}}}{49 \cdot 7 ^{\frac{4}{5}}})

将

x = 5

代入

x^{\frac{4}{5}} (x - 5)^{2} : 0

极小值 (5, 0)

极小值 (0, 0), 极大值 (\frac{10}{7}, \frac{625 \cdot 1 0 ^{\frac{4}{5}}}{49 \cdot 7 ^{\frac{4}{5}}}), 极小值 (5, 0)

作图

流行的例子

定义域 f(x)=sqrt(-x-1)+3

d o main f (x) = - x - 1 + 3

slopeintercept x+6y=2y-7

s l o p e in t erce pt x + 6 y = 2 y - 7

渐近线 (x-3)/(x^2-x-6)

a sy m pt o t es \frac{x - 3}{x ^{2} - x - 6}

直线 3x-2y=-6

l in e 3 x - 2 y = - 6

slopeintercept x-y=6

s l o p e in t erce pt x - y = 6