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

The extreme f(x)=x^{2/3}(20-x) is Minimum(0,0),Maximum(8,48)

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

extreme points

f (x) = x^{\frac{2}{3}} (20 - x)

Minimum (0, 0), Maximum (8, 48)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 8,

Decreasing

: 8 < x < \infty

Plug

x = 0

into

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

Minimum (0, 0)

Plug

x = 8

into

x^{\frac{2}{3}} (20 - x) : 48

Maximum (8, 48)

Minimum (0, 0), Maximum (8, 48)

y = x^{2} + 6 z + z^{2}

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

f (x) = 5 x^{2} y - 3 x y^{2} - 4 x + 3 y

f (x) = tan (x) [- 5, 6]

- x^{3} + x^{2} + x + 8

What is the extreme f(x)=x^{2/3}(20-x) ?
The extreme f(x)=x^{2/3}(20-x) is Minimum(0,0),Maximum(8,48)