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

The monotone f(x)= 1/(x^2+1) is Increasing:-infinity <x<0,Decreasing:0<x<infinity

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

monotone

Increasing : - \infty < x < 0, Decreasing : 0 < x < \infty

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \infty

Increasing : - \infty < x < 0, Decreasing : 0 < x < \infty

What is the monotone f(x)= 1/(x^2+1) ?
The monotone f(x)= 1/(x^2+1) is Increasing:-infinity <x<0,Decreasing:0<x<infinity