en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Functions >

extreme f(x)=(ln(x))/(2x)

Solution

extreme

Solution

Maximum (e, \frac{1}{2 e})

Solution steps

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

Find intervals:

Increasing

: 0 < x < e,

Decreasing

: e < x < \infty

Plug

x = e

into

\frac{ln ( x )}{2 x} : \frac{1}{2 e}

Maximum (e, \frac{1}{2 e})

Graph

Popular Examples

extreme f(x)=(2e^{3x})/(-2x-5)

extreme f(x)=x^4+x^2+3

extreme f(x,y)=x+sqrt(2)y

extreme 5sin^2(x)

Frequently Asked Questions (FAQ)

What is the extreme f(x)=(ln(x))/(2x) ?
The extreme f(x)=(ln(x))/(2x) is Maximum(e, 1/(2e))