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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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