What is the extreme f(x)= x/(1+x^2) ?

The extreme f(x)= x/(1+x^2) is Minimum(-1,-1/2),Maximum(1, 1/2)

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extreme f(x)= x/(1+x^2)

extreme points

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

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})

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