What is the extreme f(x)=x(x-9)^2 ?

The extreme f(x)=x(x-9)^2 is Maximum(3,108),Minimum(9,0)

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extreme f(x)=x(x-9)^2

extreme points

f (x) = x (x - 9)^{2}

Maximum (3, 108), Minimum (9, 0)

Solution steps

f^{'} (x) = 3 (x - 9) (x - 3)

Find intervals:

Increasing

: - \infty < x < 3,

Decreasing

: 3 < x < 9,

Increasing

: 9 < x < \infty

Plug

x = 3

into

x (x - 9)^{2} : 108

Maximum (3, 108)

Plug

x = 9

into

x (x - 9)^{2} : 0

Minimum (9, 0)

Maximum (3, 108), Minimum (9, 0)

f (x) = - \frac{2}{3} x^{3} + 2 x^{2} + 60

f (x) = \frac{x ( x - 4 ) ^{2}}{4}

y (t, β) = - 4 e^{- 4 t} (β + 15) + 5 e^{- 5 t} (β + 12)

f (x, y) = 2 x^{2} + 2 y^{2} - 4 y + 9

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

What is the extreme f(x)=x(x-9)^2 ?
The extreme f(x)=x(x-9)^2 is Maximum(3,108),Minimum(9,0)