en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Functions >

extreme x*ln(x)

Solution

extreme points

x \cdot ln (x)

Solution

Minimum (\frac{1}{e}, - \frac{1}{e})

Solution steps

f^{'} (x) = ln (x) + 1

Find intervals:

Decreasing

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

Increasing

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

Plug

x = \frac{1}{e}

into

x \cdot ln (x) : - \frac{1}{e}

Minimum (\frac{1}{e}, - \frac{1}{e})

Graph

Popular Examples

extreme f(x)=x^2+xy+y^2

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

extreme f(x,y)=3xy^2-2y+5x^2y^2

extreme f(x)=x^3-3x^2-9x+7

extreme x/(ln(x))

Frequently Asked Questions (FAQ)

What is the extreme x*ln(x) ?
The extreme x*ln(x) is Minimum(1/e ,-1/e)