en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Functions >

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

Solution

extreme

Solution

Minimum (1, \frac{1}{4})

Solution steps

f^{'} (x) = - \frac{3 ( x - 1 )}{x ^{2} ( x - 3 ) ^{3}}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = 1

into

\frac{1}{x ( x - 3 ) ^{2}} : \frac{1}{4}

Minimum (1, \frac{1}{4})

Graph

Popular Examples

extreme (4x)/(x^2+1)

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

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

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

extreme f(x,y)=x^2+2y^2+xy-5x-6y

Frequently Asked Questions (FAQ)

What is the extreme f(x)= 1/(x(x-3)^2) ?
The extreme f(x)= 1/(x(x-3)^2) is Minimum(1, 1/4)