What is the monotone 1-e^{-x}x^2 ?

The monotone 1-e^{-x}x^2 is Increasing:-infinity <x<0,Decreasing:0<x<2,Increasing:2<x<infinity

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monotone 1-e^{-x}x^2

monotone intervals

1 - e^{- x} x^{2}

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

Solution steps

f^{'} (x) = e^{- x} x (x - 2)

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

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

5 e^{- x}

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

f (x) = \frac{3 x - 4}{x ^{2} - 5 x + 10}

f (x) = 10 - x

g (x) = \frac{2 x}{x ^{2} - 9}

What is the monotone 1-e^{-x}x^2 ?
The monotone 1-e^{-x}x^2 is Increasing:-infinity <x<0,Decreasing:0<x<2,Increasing:2<x<infinity