What is the extreme f(x)=2x^5ln(x),(0,10) ?

The extreme f(x)=2x^5ln(x),(0,10) is Minimum(1/(\sqrt[5]{e)},-2/(5e))

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extreme f(x)=2x^5ln(x),(0,10)

extreme

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

Solution steps

Find the critical points:

x = \frac{1}{5 e}

Domain of

2 x^{5} ln (x), (0, 10) : 0 < x < 10

Find intervals:

Decreasing

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

Increasing

: \frac{1}{5 e} < x < 10

Plug the extreme point

x = \frac{1}{5 e}

into

2 x^{5} ln (x) \Rightarrow y = - \frac{2}{5 e}

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

What is the extreme f(x)=2x^5ln(x),(0,10) ?
The extreme f(x)=2x^5ln(x),(0,10) is Minimum(1/(\sqrt[5]{e)},-2/(5e))