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)

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

extreme points

f (x) = x^{2} (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} (x - 3)^{2} : 0

Minimum (0, 0)

Plug

x = \frac{3}{2}

into

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

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

Plug

x = 3

into

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

Minimum (3, 0)

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

f (x, y) = 21 x y e^{- x^{2} - y^{2}}

2 x^{3} - 3 x^{2} - x + 9

f (x) = (x - 6) e^{- 6 x}

2 t^{10} (4 - t^{2})^{5}

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

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)