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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

x^{3} + x^{2} - 9 x - 9

f (x) = - \frac{1}{2} x + \frac{5}{2}

2^{x}

f (x) = x^{2} - x + 2

2 + \frac{1}{x}

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