What is the extreme f(x)=x^{2/3}(x-7) ?

The extreme f(x)=x^{2/3}(x-7) is Maximum(0,0),Minimum(14/5 ,-(21*14^{2/3})/(5*5^{2/3)})

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extreme f(x)=x^{2/3}(x-7)

extreme

Maximum (0, 0), Minimum (\frac{14}{5}, - \frac{21 \cdot 1 4 ^{\frac{2}{3}}}{5 \cdot 5 ^{\frac{2}{3}}})

Solution steps

f^{'} (x) = \frac{5 x - 14}{3 x ^{\frac{1}{3}}}

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{14}{5},

Increasing

: \frac{14}{5} < x < \infty

Plug

x = 0

into

x^{\frac{2}{3}} (x - 7) : 0

Maximum (0, 0)

Plug

x = \frac{14}{5}

into

x^{\frac{2}{3}} (x - 7) : - \frac{21 \cdot 1 4 ^{\frac{2}{3}}}{5 \cdot 5 ^{\frac{2}{3}}}

Minimum (\frac{14}{5}, - \frac{21 \cdot 1 4 ^{\frac{2}{3}}}{5 \cdot 5 ^{\frac{2}{3}}})

Maximum (0, 0), Minimum (\frac{14}{5}, - \frac{21 \cdot 1 4 ^{\frac{2}{3}}}{5 \cdot 5 ^{\frac{2}{3}}})

What is the extreme f(x)=x^{2/3}(x-7) ?
The extreme f(x)=x^{2/3}(x-7) is Maximum(0,0),Minimum(14/5 ,-(21*14^{2/3})/(5*5^{2/3)})