What is the extreme (ln(x))/(x^8) ?

The extreme (ln(x))/(x^8) is Maximum(\sqrt[8]{e}, 1/(8e))

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extreme (ln(x))/(x^8)

extreme

Maximum (8 e, \frac{1}{8 e})

Solution steps

f^{'} (x) = \frac{1 - 8 ln ( x )}{x ^{9}}

Find intervals:

Increasing

: 0 < x < 8 e,

Decreasing

: 8 e < x < \infty

Plug

x = 8 e

into

\frac{ln ( x )}{x ^{8}} : \frac{1}{8 e}

Maximum (8 e, \frac{1}{8 e})

What is the extreme (ln(x))/(x^8) ?
The extreme (ln(x))/(x^8) is Maximum(\sqrt[8]{e}, 1/(8e))