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+81)

Solution

extreme points

\frac{x}{x ^{2} + 81}

Solution

Minimum (- 9, - \frac{1}{18}), Maximum (9, \frac{1}{18})

Solution steps

f^{'} (x) = \frac{- x ^{2} + 81}{( x ^{2} + 81 ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 9,

Increasing

: - 9 < x < 9,

Decreasing

: 9 < x < \infty

Plug

x = - 9

into

\frac{x}{x ^{2} + 81} : - \frac{1}{18}

Minimum (- 9, - \frac{1}{18})

Plug

x = 9

into

\frac{x}{x ^{2} + 81} : \frac{1}{18}

Maximum (9, \frac{1}{18})

Minimum (- 9, - \frac{1}{18}), Maximum (9, \frac{1}{18})

Graph

Popular Examples

extreme f(x)= 1/(sqrt(2pi))e^{(-x^2)/2}extreme points

f (x) = \frac{1}{2 π} e^{\frac{- x ^{2}}{2}}

extreme f(x)=(2x)/(x^2+16),-5<= x<= 5 extreme points

f (x) = \frac{2 x}{x ^{2} + 16}, - 5 \leq x \leq 5

extreme f(x)=(3+x)/(7-x),-7<= x<= 0 extreme points

f (x) = \frac{3 + x}{7 - x}, - 7 \leq x \leq 0

extreme f(x)=e^{6x^2+4y^2+10}extreme points

f (x) = e^{6 x^{2} + 4 y^{2} + 10}

extreme f(x,y)=(x^2-y^2)e^{-(x^2+y^2)}extreme points

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

Frequently Asked Questions (FAQ)

What is the extreme x/(x^2+81) ?
The extreme x/(x^2+81) is Minimum(-9,-1/18),Maximum(9, 1/18)