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Popular Functions >

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)

Graph

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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)