For which values of `x` , the function `f(x)=x/(x^2+1)` is increasing and for which values of `x` , it is decreasing.

Explanation

Given,`f(x)=x/(x^2+1)`

`f'(x)=(1−x^2​)/(x^2+1)^2`

f is strictly increasing if f′(x)>0

i.e. if`(1−x^2​)/(x^2+1)^2>0`

=`(1−x^2​)>0`

=`x^2<1`

=`−1 < x < 1`

f is increasing if −1
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