What is the extreme f(x)=x^{2/3}(20-3x) ?

The extreme f(x)=x^{2/3}(20-3x) is Minimum(0,0),Maximum(8/3 ,16*3^{1/3})

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extreme f(x)=x^{2/3}(20-3x)

extreme

Minimum (0, 0), Maximum (\frac{8}{3}, 16 \cdot 3^{\frac{1}{3}})

Solution steps

f^{'} (x) = - \frac{5 ( 3 x - 8 )}{3 x ^{\frac{1}{3}}}

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{8}{3},

Decreasing

: \frac{8}{3} < x < \infty

Plug

x = 0

into

x^{\frac{2}{3}} (20 - 3 x) : 0

Minimum (0, 0)

Plug

x = \frac{8}{3}

into

x^{\frac{2}{3}} (20 - 3 x) : 16 \cdot 3^{\frac{1}{3}}

Maximum (\frac{8}{3}, 16 \cdot 3^{\frac{1}{3}})

Minimum (0, 0), Maximum (\frac{8}{3}, 16 \cdot 3^{\frac{1}{3}})

What is the extreme f(x)=x^{2/3}(20-3x) ?
The extreme f(x)=x^{2/3}(20-3x) is Minimum(0,0),Maximum(8/3 ,16*3^{1/3})