What is the extreme f(x)=2x^5ln(x) ?

The extreme f(x)=2x^5ln(x) is Minimum(1/(\sqrt[5]{e)},-2/(5e))

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extreme f(x)=2x^5ln(x)

extreme

Minimum (\frac{1}{5 e}, - \frac{2}{5 e})

Solution steps

f^{'} (x) = 2 (5 x^{4} ln (x) + x^{4})

Find intervals:

Decreasing

: 0 < x < \frac{1}{5 e},

Increasing

: \frac{1}{5 e} < x < \infty

Plug

x = \frac{1}{5 e}

into

2 x^{5} ln (x) : - \frac{2}{5 e}

Minimum (\frac{1}{5 e}, - \frac{2}{5 e})

What is the extreme f(x)=2x^5ln(x) ?
The extreme f(x)=2x^5ln(x) is Minimum(1/(\sqrt[5]{e)},-2/(5e))