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

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

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

monotone intervals

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

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

Solution steps

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

y = \frac{3}{2} x + 2

f (x) = - 0.1 t^{2} + 0.8 t + 98.8

f (x) = \frac{x ^{2} - 6 x + 5}{x - 5}

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

f (x) = \frac{x ^{2} + 5 x + 4}{x ^{2} + 3 x + 2}

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