What is the monotone y= x/(x^2+4) ?

The monotone y= x/(x^2+4) is Decreasing:-infinity <x<-2,Increasing:-2<x<2,Decreasing:2<x<infinity

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monotone y= x/(x^2+4)

monotone intervals

y = \frac{x}{x ^{2} + 4}

Decreasing : - \infty < x < - 2, Increasing : - 2 < x < 2, Decreasing : 2 < x < \infty

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 2,

Decreasing

: 2 < x < \infty

Decreasing : - \infty < x < - 2, Increasing : - 2 < x < 2, Decreasing : 2 < x < \infty

0.001 x^{3} + 7 x + 54

y = 5 - 2 x

\frac{3 x}{x + 4}

f (x) = 6 x

f (x) = x^{4} - 4 x^{3} + 3

What is the monotone y= x/(x^2+4) ?
The monotone y= x/(x^2+4) is Decreasing:-infinity <x<-2,Increasing:-2<x<2,Decreasing:2<x<infinity