en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Functions >

extreme x/(x^2+100)

Solution

extreme

Solution

Minimum (- 10, - \frac{1}{20}), Maximum (10, \frac{1}{20})

Solution steps

f^{'} (x) = \frac{- x ^{2} + 100}{( x ^{2} + 100 ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 10,

Increasing

: - 10 < x < 10,

Decreasing

: 10 < x < \infty

Plug

x = - 10

into

\frac{x}{x ^{2} + 100} : - \frac{1}{20}

Minimum (- 10, - \frac{1}{20})

Plug

x = 10

into

\frac{x}{x ^{2} + 100} : \frac{1}{20}

Maximum (10, \frac{1}{20})

Minimum (- 10, - \frac{1}{20}), Maximum (10, \frac{1}{20})

Graph

Popular Examples

extreme f(x,y)=-x^3+4xy-2y^2+4x+1

extreme f(x)=2x+sin(4x)

extreme f(x)=-2x^2+12x-10

extreme f(x)=ye^{-x}

extreme f(x)=(x+1)/(x^2-4x-5)

Frequently Asked Questions (FAQ)

What is the extreme x/(x^2+100) ?
The extreme x/(x^2+100) is Minimum(-10,-1/20),Maximum(10, 1/20)