What is the extreme f(x)=x^3-6x^2+9 ?

The extreme f(x)=x^3-6x^2+9 is Maximum(0,9),Minimum(4,-23)

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extreme f(x)=x^3-6x^2+9

extreme points

f (x) = x^{3} - 6 x^{2} + 9

Maximum (0, 9), Minimum (4, - 23)

Solution steps

f^{'} (x) = 3 x^{2} - 12 x

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = 0

into

x^{3} - 6 x^{2} + 9 : 9

Maximum (0, 9)

Plug

x = 4

into

x^{3} - 6 x^{2} + 9 : - 23

Minimum (4, - 23)

Maximum (0, 9), Minimum (4, - 23)

What is the extreme f(x)=x^3-6x^2+9 ?
The extreme f(x)=x^3-6x^2+9 is Maximum(0,9),Minimum(4,-23)