en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=ln(2x)-2x^2

Solution

extreme points

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

Solution

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

Solution steps

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

Find intervals:

Increasing

: 0 < x < \frac{1}{2},

Decreasing

: \frac{1}{2} < x < \infty

Plug

x = \frac{1}{2}

into

ln (2 x) - 2 x^{2} : - \frac{1}{2}

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

Popular Examples

extreme f(x)=(x-6)^{2/3}extreme points

f (x) = (x - 6)^{\frac{2}{3}}

extreme (x^2+2)/(7x-4x^2)extreme points

\frac{x ^{2} + 2}{7 x - 4 x ^{2}}

extreme f(x)=-10x^2+1620x-40000 extreme points

f (x) = - 10 x^{2} + 1620 x - 40000

extreme x^3-9x^2+4 extreme points

x^{3} - 9 x^{2} + 4

extreme f(x,y)=x^3+y^3-6xy+27 extreme points

f (x, y) = x^{3} + y^{3} - 6 x y + 27

Frequently Asked Questions (FAQ)

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