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)=x^2-8ln(x)

Solution

extreme

Solution

Minimum (2, 4 - 8 ln (2))

Solution steps

f^{'} (x) = 2 x - \frac{8}{x}

Find intervals:

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = 2

into

x^{2} - 8 ln (x) : 4 - 8 ln (2)

Minimum (2, 4 - 8 ln (2))

Graph

Popular Examples

extreme f(x)=3x^2e^x

extreme f(x)=4y^2-5x=2y-3y^2

extreme f(x,y)=x^3-y^3-6xy-4

extreme f(x)=(2(x+2)^2)/(x^2)

extreme f(x,y)=2x^3-2y^3+12xy+3

Frequently Asked Questions (FAQ)

What is the extreme f(x)=x^2-8ln(x) ?
The extreme f(x)=x^2-8ln(x) is Minimum(2,4-8ln(2))