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 points

f (x) = x^{\frac{2}{3}} (x + 4)

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)

f (x, y, λ) = x^{2} + y^{2} - (x + 2 y - 5)

f (x) = 7 x^{4} - 28 x^{3 + 7}

(\frac{3}{2})^{x}

f (x) = \frac{x ^{3} - 1}{x ^{3} + 1}

f (x, y) = 2 x^{2} - 5 x + 6 y + 2 y^{2}

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)