What is the monotone f(x)=x*e^{1/x} ?

The monotone f(x)=x*e^{1/x} is Increasing:-infinity <x<0,Decreasing:0<x<1,Increasing:1<x<infinity

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monotone f(x)=x*e^{1/x}

monotone

Increasing : - \infty < x < 0, Decreasing : 0 < x < 1, Increasing : 1 < x < \infty

Solution steps

Find the critical points:

x = 1

Domain of

x \cdot e^{\frac{1}{x}} : x < 0 or x > 0

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Increasing : - \infty < x < 0, Decreasing : 0 < x < 1, Increasing : 1 < x < \infty

What is the monotone f(x)=x*e^{1/x} ?
The monotone f(x)=x*e^{1/x} is Increasing:-infinity <x<0,Decreasing:0<x<1,Increasing:1<x<infinity