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)=16x+9/x

Solution

extreme

Solution

Maximum (- \frac{3}{4}, - 24), Minimum (\frac{3}{4}, 24)

Solution steps

f^{'} (x) = 16 - \frac{9}{x ^{2}}

Find intervals:

Increasing

: - \infty < x < - \frac{3}{4},

Decreasing

: - \frac{3}{4} < x < 0,

Decreasing

: 0 < x < \frac{3}{4},

Increasing

: \frac{3}{4} < x < \infty

Plug

x = - \frac{3}{4}

into

16 x + \frac{9}{x} : - 24

Maximum (- \frac{3}{4}, - 24)

Plug

x = \frac{3}{4}

into

16 x + \frac{9}{x} : 24

Minimum (\frac{3}{4}, 24)

Maximum (- \frac{3}{4}, - 24), Minimum (\frac{3}{4}, 24)

Graph

Popular Examples

extreme f(x)=x+(22)/x

extreme y=6x-7x^{6/7}

extreme f(x,y)=ln(sqrt(x^2+y^2-64))

extreme (x+6)^{2/3}

extreme x^2y^2-x-y

Frequently Asked Questions (FAQ)

What is the extreme f(x)=16x+9/x ?
The extreme f(x)=16x+9/x is Maximum(-3/4 ,-24),Minimum(3/4 ,24)