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

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

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monotone y=(x^2)/((x-2)^2)

monotone intervals

y = \frac{x ^{2}}{( x - 2 ) ^{2}}

Decreasing : - \infty < x < 0, Increasing : 0 < x < 2, Decreasing : 2 < x < \infty

Solution steps

f^{'} (x) = - \frac{4 x}{( x - 2 ) ^{3}}

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Decreasing : - \infty < x < 0, Increasing : 0 < x < 2, Decreasing : 2 < x < \infty

- 2 x - 1

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

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

1 - x^{2}

(- 4, 6), (8, - 6)

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