What is the extreme f(x)=x(x-2)^2 ?

The extreme f(x)=x(x-2)^2 is Maximum(2/3 , 32/27),Minimum(2,0)

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extreme f(x)=x(x-2)^2

extreme points

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

Maximum (\frac{2}{3}, \frac{32}{27}), Minimum (2, 0)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < \frac{2}{3},

Decreasing

: \frac{2}{3} < x < 2,

Increasing

: 2 < x < \infty

Plug

x = \frac{2}{3}

into

x (x - 2)^{2} : \frac{32}{27}

Maximum (\frac{2}{3}, \frac{32}{27})

Plug

x = 2

into

x (x - 2)^{2} : 0

Minimum (2, 0)

Maximum (\frac{2}{3}, \frac{32}{27}), Minimum (2, 0)

f (x, y) = x^{3} - 6 x y + 8 y^{3}

f (x, y) = x^{2} + x^{2} y + y^{2} + 1

f (x) = 2 x + cos (x)

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

f (x) = x^{2} - 12 x

What is the extreme f(x)=x(x-2)^2 ?
The extreme f(x)=x(x-2)^2 is Maximum(2/3 , 32/27),Minimum(2,0)