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Popular >

extreme f(x)=(ln(2x))/x

Solution

extreme points

f (x) = \frac{ln ( 2 x )}{x}

Solution

Maximum (\frac{e}{2}, \frac{2}{e})

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Plug

x = \frac{e}{2}

into

\frac{ln ( 2 x )}{x} : \frac{2}{e}

Maximum (\frac{e}{2}, \frac{2}{e})

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=(ln(2x))/x ?
The extreme f(x)=(ln(2x))/x is Maximum(e/2 , 2/e)