en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Functions >

extreme 1/x+ln(x)

Solution

extreme points

\frac{1}{x} + ln (x)

Solution

Minimum (1, 1)

Solution steps

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

Find intervals:

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = 1

into

\frac{1}{x} + ln (x) : 1

Minimum (1, 1)

Graph

Popular Examples

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

extreme f(x,y)=y^2e^{-x+ln(y)}

extreme f(x,y)=x^3+y^3-15xy

extreme f(x,y)=sqrt(49-x^2-y^2)

extreme f(x,y)=xy+y^2e^{2x}

Frequently Asked Questions (FAQ)

What is the extreme 1/x+ln(x) ?
The extreme 1/x+ln(x) is Minimum(1,1)