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

The extreme f(x)=9x^2-x^3-3 is Minimum(0,-3),Maximum(6,105)

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

extreme points

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

Minimum (0, - 3), Maximum (6, 105)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 6,

Decreasing

: 6 < x < \infty

Plug

x = 0

into

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

Minimum (0, - 3)

Plug

x = 6

into

9 x^{2} - x^{3} - 3 : 105

Maximum (6, 105)

Minimum (0, - 3), Maximum (6, 105)

What is the extreme f(x)=9x^2-x^3-3 ?
The extreme f(x)=9x^2-x^3-3 is Minimum(0,-3),Maximum(6,105)