What is the extreme f(x)=x^2*(x-3)^2 ?

The extreme f(x)=x^2*(x-3)^2 is Minimum(0,0),Maximum(3/2 , 81/16),Minimum(3,0)

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extreme f(x)=x^2*(x-3)^2

extreme points

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

Minimum (0, 0), Maximum (\frac{3}{2}, \frac{81}{16}), Minimum (3, 0)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

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

Decreasing

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

Increasing

: 3 < x < \infty

Plug

x = 0

into

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

Minimum (0, 0)

Plug

x = \frac{3}{2}

into

x^{2} \cdot (x - 3)^{2} : \frac{81}{16}

Maximum (\frac{3}{2}, \frac{81}{16})

Plug

x = 3

into

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

Minimum (3, 0)

Minimum (0, 0), Maximum (\frac{3}{2}, \frac{81}{16}), Minimum (3, 0)

- x^{2} + 4

1512 x - 0.14 x^{3}

- x^{2} - 1

f (x) = (x^{2} - 8)^{3} + 50

f (y) = x^{2} + x - 30

What is the extreme f(x)=x^2*(x-3)^2 ?
The extreme f(x)=x^2*(x-3)^2 is Minimum(0,0),Maximum(3/2 , 81/16),Minimum(3,0)