What is the extreme f(x)=x^{2/3 (x-3)} ?

The extreme f(x)=x^{2/3 (x-3)} is Minimum(3/(\W_{0)(3e)},(3/(\W_{0)(3e)})^{2/(\W_{0)(3e)}-2})

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extreme f(x)=x^{2/3 (x-3)}

extreme

Minimum (\frac{3}{W _{0} ( 3 e )}, (\frac{3}{W _{0} ( 3 e )})^{\frac{2}{W _{0} ( 3 e )} - 2})

Solution steps

Find the critical points:

x = \frac{3}{W _{0} ( 3 e )}

Domain of

x^{\frac{2}{3} (x - 3)} : x > 0

Find intervals:

Decreasing

: 0 < x < \frac{3}{W _{0} ( 3 e )},

Increasing

: \frac{3}{W _{0} ( 3 e )} < x < \infty

Plug the extreme point

x = \frac{3}{W _{0} ( 3 e )}

into

x^{\frac{2}{3} (x - 3)} \Rightarrow y = (\frac{3}{W _{0} ( 3 e )})^{\frac{2}{W _{0} ( 3 e )} - 2}

Minimum (\frac{3}{W _{0} ( 3 e )}, (\frac{3}{W _{0} ( 3 e )})^{\frac{2}{W _{0} ( 3 e )} - 2})

What is the extreme f(x)=x^{2/3 (x-3)} ?
The extreme f(x)=x^{2/3 (x-3)} is Minimum(3/(\W_{0)(3e)},(3/(\W_{0)(3e)})^{2/(\W_{0)(3e)}-2})