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

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

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

monotone intervals

f (x) = x^{(\frac{1}{x})}

Increasing : 0 < x < e, Decreasing : e < x < \infty

Solution steps

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

Find intervals:

Increasing

: 0 < x < e,

Decreasing

: e < x < \infty

Increasing : 0 < x < e, Decreasing : e < x < \infty

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