en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme (ln(4x))/x

Solution

extreme points

\frac{ln ( 4 x )}{x}

Solution

Maximum (\frac{e}{4}, \frac{4}{e})

Solution steps

f^{'} (x) = \frac{1 - ln ( 4 x )}{x ^{2}}

Find intervals:

Increasing

: 0 < x < \frac{e}{4},

Decreasing

: \frac{e}{4} < x < \infty

Plug

x = \frac{e}{4}

into

\frac{ln ( 4 x )}{x} : \frac{4}{e}

Maximum (\frac{e}{4}, \frac{4}{e})

Popular Examples

extreme f(x)= 4/(x-3)extreme points

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

extreme f(x,y)=x^2+2y^2+2x-3 extreme points

f (x, y) = x^{2} + 2 y^{2} + 2 x - 3

extreme f(x)=19+4x-x^2 extreme points

f (x) = 19 + 4 x - x^{2}

extreme f(x,y)=x^3+3x^2y+y^3-y extreme points

f (x, y) = x^{3} + 3 x^{2} y + y^{3} - y

extreme f(x)=e^x+e^{-x}extreme points

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

Frequently Asked Questions (FAQ)

What is the extreme (ln(4x))/x ?
The extreme (ln(4x))/x is Maximum(e/4 , 4/e)