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

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

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

extreme points

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

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

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

Increasing

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

Plug

x = 0

into

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

Maximum (0, 0)

Plug

x = \frac{2}{5}

into

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

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

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

\frac{x}{( x + 1 ) ^{2}}

f (x) = - x^{4} + 8 x^{3} - 18 x^{2}

- 4 x^{2} + 2 y^{2} - 2 x y

f (x, y) = - 2 x^{2} - y^{2} + x y + 8 x + 3 y

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

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