What is the extreme (ln(x))/(x^3) ?

The extreme (ln(x))/(x^3) is Maximum(\sqrt[3]{e}, 1/(3e))

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extreme (ln(x))/(x^3)

extreme points

\frac{ln ( x )}{x ^{3}}

Maximum (3 e, \frac{1}{3 e})

Solution steps

f^{'} (x) = \frac{1 - 3 ln ( x )}{x ^{4}}

Find intervals:

Increasing

: 0 < x < 3 e,

Decreasing

: 3 e < x < \infty

Plug

x = 3 e

into

\frac{ln ( x )}{x ^{3}} : \frac{1}{3 e}

Maximum (3 e, \frac{1}{3 e})

f (x) = - (25 - x^{2})^{2}

f (x) = (x - 3)^{\frac{4}{3}}

- \frac{5}{x - 6}

f (x, y) = x^{2} - 6 x y + y^{2} + 16 y + 9

f (x y) = x y + 4 x

What is the extreme (ln(x))/(x^3) ?
The extreme (ln(x))/(x^3) is Maximum(\sqrt[3]{e}, 1/(3e))