What is the monotone xe^{-(x^2)/2} ?

The monotone xe^{-(x^2)/2} is Decreasing:-infinity <x<-1,Increasing:-1<x<1,Decreasing:1<x<infinity

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monotone xe^{-(x^2)/2}

monotone

Decreasing : - \infty < x < - 1, Increasing : - 1 < x < 1, Decreasing : 1 < x < \infty

Solution steps

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

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 xe^{-(x^2)/2} ?
The monotone xe^{-(x^2)/2} is Decreasing:-infinity <x<-1,Increasing:-1<x<1,Decreasing:1<x<infinity