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Popular Functions >

extreme x/(1+x^2)

Solution

extreme points

\frac{x}{1 + x ^{2}}

Solution

Minimum (- 1, - \frac{1}{2}), Maximum (1, \frac{1}{2})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

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

Minimum (- 1, - \frac{1}{2})

Plug

x = 1

into

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

Maximum (1, \frac{1}{2})

Minimum (- 1, - \frac{1}{2}), Maximum (1, \frac{1}{2})

Graph

Popular Examples

extreme f(x)=9x^{2/3}+3x-6

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

extreme f(x,y)=3x^2+2y^2

extreme f(x,y)=x-y

extreme f(x,y)=y^4+x^2-8y^2+2x

Frequently Asked Questions (FAQ)

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