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Popular >

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

Solution

extreme points

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

Solution

Maximum (e, \frac{1}{2 e})

Solution steps

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

Find intervals:

Increasing

: 0 < x < e,

Decreasing

: e < x < \infty

Plug

x = e

into

\frac{ln ( x )}{2 x} : \frac{1}{2 e}

Maximum (e, \frac{1}{2 e})

Graph

Popular Examples

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extreme f(x)=x^4-5x^3-15x^2 extreme points

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=(ln(x))/(2x) ?
The extreme f(x)=(ln(x))/(2x) is Maximum(e, 1/(2e))