en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme x+1/x

Solution

extreme points

x + \frac{1}{x}

Solution

Maximum (- 1, - 2), Minimum (1, 2)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

x + \frac{1}{x} : - 2

Maximum (- 1, - 2)

Plug

x = 1

into

x + \frac{1}{x} : 2

Minimum (1, 2)

Maximum (- 1, - 2), Minimum (1, 2)

Popular Examples

domain of f(x)=(-2x+15)/(x^2+5x)domain

f (x) = \frac{- 2 x + 15}{x ^{2} + 5 x}

inverse of x+2 inverse

x + 2

periodicity of y=sin(1/4 x)periodicity

y = sin (\frac{1}{4} x)

distance (2,0),(-4,5)distance

(2, 0), (- 4, 5)

perpendicular y=-2x+4,(0,-3)perpendicular

y = - 2 x + 4, (0, - 3)

Frequently Asked Questions (FAQ)

What is the extreme x+1/x ?
The extreme x+1/x is Maximum(-1,-2),Minimum(1,2)