What is the extreme f(x)=x^{2/3}(x+1) ?

The extreme f(x)=x^{2/3}(x+1) is Maximum(-2/5 ,(3(-2/5)^{2/3})/5),Minimum(0,0)

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extreme f(x)=x^{2/3}(x+1)

extreme points

f (x) = x^{\frac{2}{3}} (x + 1)

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

Solution steps

f^{'} (x) = \frac{5 x + 2}{3 x ^{\frac{1}{3}}}

Find intervals:

Increasing

: - \infty < x < - \frac{2}{5},

Decreasing

: - \frac{2}{5} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{2}{5}

into

x^{\frac{2}{3}} (x + 1) : \frac{3 ( - \frac{2}{5} ) ^{\frac{2}{3}}}{5}

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

Plug

x = 0

into

x^{\frac{2}{3}} (x + 1) : 0

Minimum (0, 0)

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

f (x) = x^{2} + 4 x (\frac{4000}{x ^{2}})

f (x) = (1)^{\frac{1}{3}} \cdot (- 9)

f (x) = - 2 x^{2} - x

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

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

What is the extreme f(x)=x^{2/3}(x+1) ?
The extreme f(x)=x^{2/3}(x+1) is Maximum(-2/5 ,(3(-2/5)^{2/3})/5),Minimum(0,0)