What is the extreme f(x)=x^{-7}ln(x) ?

The extreme f(x)=x^{-7}ln(x) is Maximum(\sqrt[7]{e}, 1/(7e))

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extreme f(x)=x^{-7}ln(x)

extreme

Maximum (7 e, \frac{1}{7 e})

Solution steps

f^{'} (x) = \frac{- 7 ln ( x ) + 1}{x ^{8}}

Find intervals:

Increasing

: 0 < x < 7 e,

Decreasing

: 7 e < x < \infty

Plug

x = 7 e

into

x^{- 7} ln (x) : \frac{1}{7 e}

Maximum (7 e, \frac{1}{7 e})

What is the extreme f(x)=x^{-7}ln(x) ?
The extreme f(x)=x^{-7}ln(x) is Maximum(\sqrt[7]{e}, 1/(7e))