What is the extreme f(x)=x^3-12x^2-27x+3 ?

The extreme f(x)=x^3-12x^2-27x+3 is Maximum(-1,17),Minimum(9,-483)

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extreme f(x)=x^3-12x^2-27x+3

extreme points

f (x) = x^{3} - 12 x^{2} - 27 x + 3

Maximum (- 1, 17), Minimum (9, - 483)

Solution steps

f^{'} (x) = 3 x^{2} - 24 x - 27

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 9,

Increasing

: 9 < x < \infty

Plug

x = - 1

into

x^{3} - 12 x^{2} - 27 x + 3 : 17

Maximum (- 1, 17)

Plug

x = 9

into

x^{3} - 12 x^{2} - 27 x + 3 : - 483

Minimum (9, - 483)

Maximum (- 1, 17), Minimum (9, - 483)

y = - 3 (x - 1)

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

(1, 8), (6, 23)

f (x) = x^{2} + 18 x + 81

- x + 5

What is the extreme f(x)=x^3-12x^2-27x+3 ?
The extreme f(x)=x^3-12x^2-27x+3 is Maximum(-1,17),Minimum(9,-483)