What is the extreme f(x)=-6x^2-12x-9,-3<= x<= 2 ?

The extreme f(x)=-6x^2-12x-9,-3<= x<= 2 is Minimum(-3,-27),Maximum(-1,-3),Minimum(2,-57)

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extreme f(x)=-6x^2-12x-9,-3<= x<= 2

extreme points

f (x) = - 6 x^{2} - 12 x - 9, - 3 \leq x \leq 2

Minimum (- 3, - 27), Maximum (- 1, - 3), Minimum (2, - 57)

Solution steps

Find the critical points:

x = - 3, x = - 1, x = 2

Domain of

- 6 x^{2} - 12 x - 9, - 3 \leq x \leq 2 : - 3 \leq x \leq 2

Find intervals:

Increasing

: - 3 < x < - 1,

Decreasing

: - 1 < x < 2

Plug the extreme point

x = - 3

into

- 6 x^{2} - 12 x - 9 \Rightarrow y = - 27

Minimum (- 3, - 27)

Plug the extreme point

x = - 1

into

- 6 x^{2} - 12 x - 9 \Rightarrow y = - 3

Maximum (- 1, - 3)

Plug the extreme point

x = 2

into

- 6 x^{2} - 12 x - 9 \Rightarrow y = - 57

Minimum (2, - 57)

Minimum (- 3, - 27), Maximum (- 1, - 3), Minimum (2, - 57)

f (x) = (\frac{1}{2} x) + 3

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

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

f (x) = - 25 x^{2} - 30 y^{2} + 500 x + 300 y + 150

f (x, y) = - y^{3} + y x^{2} - 2 y^{2} x^{2} + 2 x^{4}

What is the extreme f(x)=-6x^2-12x-9,-3<= x<= 2 ?
The extreme f(x)=-6x^2-12x-9,-3<= x<= 2 is Minimum(-3,-27),Maximum(-1,-3),Minimum(2,-57)