en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme x/(x^2+16)

Solution

extreme points

\frac{x}{x ^{2} + 16}

Solution

Minimum (- 4, - \frac{1}{8}), Maximum (4, \frac{1}{8})

Solution steps

f^{'} (x) = \frac{- x ^{2} + 16}{( x ^{2} + 16 ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 4,

Increasing

: - 4 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = - 4

into

\frac{x}{x ^{2} + 16} : - \frac{1}{8}

Minimum (- 4, - \frac{1}{8})

Plug

x = 4

into

\frac{x}{x ^{2} + 16} : \frac{1}{8}

Maximum (4, \frac{1}{8})

Minimum (- 4, - \frac{1}{8}), Maximum (4, \frac{1}{8})

Graph

Popular Examples

extreme f(x)=-4cos(3x)-4 extreme points

f (x) = - 4 cos (3 x) - 4

extreme f(x,y)=200y^2+x^2-x^2y extreme points

f (x, y) = 200 y^{2} + x^{2} - x^{2} y

extreme 2x^4-16x^2+3 extreme points

2 x^{4} - 16 x^{2} + 3

extreme F(Y,Z)=Y+YZ extreme points

F (Y, Z) = Y + Y Z

extreme f(x,y)=14x^2-2x^3+4xy extreme points

f (x, y) = 14 x^{2} - 2 x^{3} + 4 x y

Frequently Asked Questions (FAQ)

What is the extreme x/(x^2+16) ?
The extreme x/(x^2+16) is Minimum(-4,-1/8),Maximum(4, 1/8)