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Popular >

monotone x^{1/x}

Solution

monotone intervals

x^{\frac{1}{x}}

Solution

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

Popular Examples

range of f(x)=(1/2)^{2x}+5 range

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

slope of y=-3x+8 slope

y = - 3 x + 8

inverse of f(x)=\sqrt[3]{(x+3)/2}inverse

domain of f(x)=(x^2-4)/(x-3)domain

f (x) = \frac{x ^{2} - 4}{x - 3}

extreme f(x)=(x-4)^{2/3}extreme points

f (x) = (x - 4)^{\frac{2}{3}}

Frequently Asked Questions (FAQ)

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