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

The extreme f(x)=x^{(2/3)}(x-3) is Maximum(0,0),Minimum(6/5 ,-(9*6^{2/3})/(5*5^{2/3)})

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

extreme points

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

Maximum (0, 0), Minimum (\frac{6}{5}, - \frac{9 \cdot 6 ^{\frac{2}{3}}}{5 \cdot 5 ^{\frac{2}{3}}})

Solution steps

f^{'} (x) = \frac{5 x - 6}{3 x ^{\frac{1}{3}}}

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{6}{5},

Increasing

: \frac{6}{5} < x < \infty

Plug

x = 0

into

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

Maximum (0, 0)

Plug

x = \frac{6}{5}

into

x^{\frac{2}{3}} (x - 3) : - \frac{9 \cdot 6 ^{\frac{2}{3}}}{5 \cdot 5 ^{\frac{2}{3}}}

Minimum (\frac{6}{5}, - \frac{9 \cdot 6 ^{\frac{2}{3}}}{5 \cdot 5 ^{\frac{2}{3}}})

Maximum (0, 0), Minimum (\frac{6}{5}, - \frac{9 \cdot 6 ^{\frac{2}{3}}}{5 \cdot 5 ^{\frac{2}{3}}})

f (x) = 6 x^{3} + 54 x^{2} + 144 x + 54

(x - 7) (x^{2} - 14 x - 98)

y = (4 - x) \cdot 4^{x}

f (x) = 3 + 3 x - 3 x^{2}, 0 \leq x \leq 3

100

What is the extreme f(x)=x^{(2/3)}(x-3) ?
The extreme f(x)=x^{(2/3)}(x-3) is Maximum(0,0),Minimum(6/5 ,-(9*6^{2/3})/(5*5^{2/3)})