What is the extreme f(x)=(ln(x))/(x^{10)} ?

The extreme f(x)=(ln(x))/(x^{10)} is Maximum(\sqrt[10]{e}, 1/(10e))

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extreme f(x)=(ln(x))/(x^{10)}

extreme

Maximum (10 e, \frac{1}{10 e})

Solution steps

f^{'} (x) = \frac{1 - 10 ln ( x )}{x ^{11}}

Find intervals:

Increasing

: 0 < x < 10 e,

Decreasing

: 10 e < x < \infty

Plug

x = 10 e

into

\frac{ln ( x )}{x ^{10}} : \frac{1}{10 e}

Maximum (10 e, \frac{1}{10 e})

What is the extreme f(x)=(ln(x))/(x^{10)} ?
The extreme f(x)=(ln(x))/(x^{10)} is Maximum(\sqrt[10]{e}, 1/(10e))