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

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

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