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

The extreme f(x)=x^2(x-2)^2 is Minimum(0,0),Maximum(1,1),Minimum(2,0)

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

extreme points

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

Minimum (0, 0), Maximum (1, 1), Minimum (2, 0)

Solution steps

f^{'} (x) = 4 x (x - 2) (x - 1)

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = 0

into

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

Minimum (0, 0)

Plug

x = 1

into

x^{2} (x - 2)^{2} : 1

Maximum (1, 1)

Plug

x = 2

into

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

Minimum (2, 0)

Minimum (0, 0), Maximum (1, 1), Minimum (2, 0)

f (x) = \frac{2}{5} x^{5} - 5 x^{4} + 16 x^{3} + 2

f (x, y) = x^{2} + x y + y^{2} - 19 y + 120

f (x) = x^{4} + 8 x^{3}

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

x^{4} - 3 x^{3}

What is the extreme f(x)=x^2(x-2)^2 ?
The extreme f(x)=x^2(x-2)^2 is Minimum(0,0),Maximum(1,1),Minimum(2,0)