What is the extreme f(x)=x^2log_{6}(x) ?

The extreme f(x)=x^2log_{6}(x) is Minimum(1/(sqrt(e)),-1/(2e)log_{6}(e))

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extreme f(x)=x^2log_{6}(x)

extreme

Minimum (\frac{1}{e}, - \frac{1}{2 e} lo g_{6} (e))

Solution steps

f^{'} (x) = \frac{x + 2 x ln ( x )}{ln ( 6 )}

Find intervals:

Decreasing

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

Increasing

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

Plug

x = \frac{1}{e}

into

x^{2} lo g_{6} (x) : - \frac{1}{2 e} lo g_{6} (e)

Minimum (\frac{1}{e}, - \frac{1}{2 e} lo g_{6} (e))

What is the extreme f(x)=x^2log_{6}(x) ?
The extreme f(x)=x^2log_{6}(x) is Minimum(1/(sqrt(e)),-1/(2e)log_{6}(e))