What is the extreme f(x)=x^{2/3}(x+4) ?

The extreme f(x)=x^{2/3}(x+4) is Maximum(-8/5 ,(12(-8/5)^{2/3})/5),Minimum(0,0)

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extreme f(x)=x^{2/3}(x+4)

extreme

Maximum - \frac{8}{5}, \frac{12 ( - \frac{8}{5} ) ^{\frac{2}{3}}}{5}, Minimum (0, 0)

Solution steps

f^{'} (x) = \frac{5 x + 8}{3 x ^{\frac{1}{3}}}

Find intervals:

Increasing

: - \infty < x < - \frac{8}{5},

Decreasing

: - \frac{8}{5} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{8}{5}

into

x^{\frac{2}{3}} (x + 4) : \frac{12 ( - \frac{8}{5} ) ^{\frac{2}{3}}}{5}

Maximum - \frac{8}{5}, \frac{12 ( - \frac{8}{5} ) ^{\frac{2}{3}}}{5}

Plug

x = 0

into

x^{\frac{2}{3}} (x + 4) : 0

Minimum (0, 0)

Maximum - \frac{8}{5}, \frac{12 ( - \frac{8}{5} ) ^{\frac{2}{3}}}{5}, Minimum (0, 0)

What is the extreme f(x)=x^{2/3}(x+4) ?
The extreme f(x)=x^{2/3}(x+4) is Maximum(-8/5 ,(12(-8/5)^{2/3})/5),Minimum(0,0)