What is the extreme x^2-6x-6,-1<= x<= 6 ?

The extreme x^2-6x-6,-1<= x<= 6 is Maximum(-1,1),Minimum(3,-15),Maximum(6,-6)

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extreme x^2-6x-6,-1<= x<= 6

extreme points

x^{2} - 6 x - 6, - 1 \leq x \leq 6

Maximum (- 1, 1), Minimum (3, - 15), Maximum (6, - 6)

Solution steps

Find the critical points:

x = - 1, x = 3, x = 6

Domain of

x^{2} - 6 x - 6, - 1 \leq x \leq 6 : - 1 \leq x \leq 6

Find intervals:

Decreasing

: - 1 < x < 3,

Increasing

: 3 < x < 6

Plug the extreme point

x = - 1

into

x^{2} - 6 x - 6 \Rightarrow y = 1

Maximum (- 1, 1)

Plug the extreme point

x = 3

into

x^{2} - 6 x - 6 \Rightarrow y = - 15

Minimum (3, - 15)

Plug the extreme point

x = 6

into

x^{2} - 6 x - 6 \Rightarrow y = - 6

Maximum (6, - 6)

Maximum (- 1, 1), Minimum (3, - 15), Maximum (6, - 6)

(x + 3) (x - 3)^{2}

x^{3} - 6 x y + y^{2} + 15 x + 4

f (x) = (\frac{1}{12} x^{3} - \frac{1}{2} x^{2} - 12)

50 - 3 x^{2} - 4 x + 2 x y - 8 y^{2} + 78 y

- 3 x^{2} + 12 x + 120

What is the extreme x^2-6x-6,-1<= x<= 6 ?
The extreme x^2-6x-6,-1<= x<= 6 is Maximum(-1,1),Minimum(3,-15),Maximum(6,-6)