en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=x+9/x

Solution

extreme points

f (x) = x + \frac{9}{x}

Solution

Maximum (- 3, - 6), Minimum (3, 6)

Solution steps

f^{'} (x) = 1 - \frac{9}{x ^{2}}

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

x + \frac{9}{x} : - 6

Maximum (- 3, - 6)

Plug

x = 3

into

x + \frac{9}{x} : 6

Minimum (3, 6)

Maximum (- 3, - 6), Minimum (3, 6)

Popular Examples

intercepts of-3x^2-6x+2 intercepts

- 3 x^{2} - 6 x + 2

asymptotes of f(x)= x/(x-5)asymptotes

f (x) = \frac{x}{x - 5}

periodicity of f(x)=3sin((xpi)/2)+2 periodicity

f (x) = 3 sin (\frac{x π}{2}) + 2

parity (3x^2)/(1-x-x^5)parity

\frac{3 x ^{2}}{1 - x - x ^{5}}

critical f(x)=(x-5)^{2/3}critical points

f (x) = (x - 5)^{\frac{2}{3}}

Frequently Asked Questions (FAQ)

What is the extreme f(x)=x+9/x ?
The extreme f(x)=x+9/x is Maximum(-3,-6),Minimum(3,6)