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

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

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

extreme points

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

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

Solution steps

f^{'} (x) = - 4 x^{3} + 18 x^{2} - 18 x

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

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

Increasing

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

Decreasing

: 3 < x < \infty

Plug

x = 0

into

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

Maximum (0, 0)

Plug

x = \frac{3}{2}

into

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

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

Plug

x = 3

into

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

Maximum (3, 0)

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

f (x) = 3 x^{3} - 5 x

f (x, y) = \frac{1}{1 - x ^{2} - y ^{2}}

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

a^{3} y = x^{3} (4 a - 3 x)

f (x) = x y

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