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Popular >

extreme f(x)=36x+9/x

Solution

extreme points

f (x) = 36 x + \frac{9}{x}

Solution

Maximum (- \frac{1}{2}, - 36), Minimum (\frac{1}{2}, 36)

Solution steps

f^{'} (x) = 36 - \frac{9}{x ^{2}}

Find intervals:

Increasing

: - \infty < x < - \frac{1}{2},

Decreasing

: - \frac{1}{2} < x < 0,

Decreasing

: 0 < x < \frac{1}{2},

Increasing

: \frac{1}{2} < x < \infty

Plug

x = - \frac{1}{2}

into

36 x + \frac{9}{x} : - 36

Maximum (- \frac{1}{2}, - 36)

Plug

x = \frac{1}{2}

into

36 x + \frac{9}{x} : 36

Minimum (\frac{1}{2}, 36)

Maximum (- \frac{1}{2}, - 36), Minimum (\frac{1}{2}, 36)

Popular Examples

domain of f(x)= 1/(x^2-x-90)domain

f (x) = \frac{1}{x ^{2} - x - 90}

inverse of f(x)=((x-1))/((x+2))inverse

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

domain of f(x)=(x+7)/(x^2-x-56)domain

f (x) = \frac{x + 7}{x ^{2} - x - 56}

slope ofintercept 0.5*80+25 slope intercept

0.5 \cdot 80 + 25

inverse of f(x)=65 inverse

f (x) = 65

Frequently Asked Questions (FAQ)

What is the extreme f(x)=36x+9/x ?
The extreme f(x)=36x+9/x is Maximum(-1/2 ,-36),Minimum(1/2 ,36)