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Popular >

extreme (2x-ln(3x))/x

Solution

extreme points

\frac{2 x - ln ( 3 x )}{x}

Solution

Minimum (\frac{e}{3}, \frac{2 e - 3}{e})

Solution steps

f^{'} (x) = \frac{ln ( 3 x ) - 1}{x ^{2}}

Find intervals:

Decreasing

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

Increasing

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

Plug

x = \frac{e}{3}

into

\frac{2 x - ln ( 3 x )}{x} : \frac{2 e - 3}{e}

Minimum (\frac{e}{3}, \frac{2 e - 3}{e})

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Frequently Asked Questions (FAQ)

What is the extreme (2x-ln(3x))/x ?
The extreme (2x-ln(3x))/x is Minimum(e/3 ,(2e-3)/e)