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Popular Functions >

extreme f(x)= 1/(x(x-6))

Solution

extreme points

f (x) = \frac{1}{x ( x - 6 )}

Solution

Maximum (3, - \frac{1}{9})

Solution steps

f^{'} (x) = - \frac{2 x - 6}{x ^{2} ( x - 6 ) ^{2}}

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 3,

Decreasing

: 3 < x < 6,

Decreasing

: 6 < x < \infty

Plug

x = 3

into

\frac{1}{x ( x - 6 )} : - \frac{1}{9}

Maximum (3, - \frac{1}{9})

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x)= 1/(x(x-6)) ?
The extreme f(x)= 1/(x(x-6)) is Maximum(3,-1/9)