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

The monotone f(x)= x/(1+x^2) is Decreasing:-infinity <x<-1,Increasing:-1<x<1,Decreasing:1<x<infinity

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

monotone intervals

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

Decreasing : - \infty < x < - 1, Increasing : - 1 < x < 1, Decreasing : 1 < x < \infty

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

Decreasing : - \infty < x < - 1, Increasing : - 1 < x < 1, Decreasing : 1 < x < \infty

3 x^{2} - 12 x

y = 2 x + 4

y = 5 - x

f (x) = \frac{4 x ^{2}}{x ^{2} - 9}

\frac{1}{2} x^{3} - 2 x^{2} - 1

What is the monotone f(x)= x/(1+x^2) ?
The monotone f(x)= x/(1+x^2) is Decreasing:-infinity <x<-1,Increasing:-1<x<1,Decreasing:1<x<infinity