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 points

\frac{ln ( x )}{x ^{8}}

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})

f (x) = (sin (x)) (cos (x))

f (x) = 2 x^{3} - 24 x^{2} + 72 x, 1 \leq x \leq 7

\frac{d}{d x} (- 21 x^{2} - 3 x_{+} 8)

f (x) = 2 sec (x) + tan (x)

f (x) = 3 x - 6 cos (x), - 2 \leq x \leq 0

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