What is the extreme y=5-2x^2,-4<= x<= 2 ?

The extreme y=5-2x^2,-4<= x<= 2 is Minimum(-4,-27),Maximum(0,5),Minimum(2,-3)

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extreme y=5-2x^2,-4<= x<= 2

extreme

Minimum (- 4, - 27), Maximum (0, 5), Minimum (2, - 3)

Solution steps

Find the critical points:

x = - 4, x = 0, x = 2

Domain of

5 - 2 x^{2}, - 4 \leq x \leq 2 : - 4 \leq x \leq 2

Find intervals:

Increasing

: - 4 < x < 0,

Decreasing

: 0 < x < 2

Plug the extreme point

x = - 4

into

5 - 2 x^{2} \Rightarrow y = - 27

Minimum (- 4, - 27)

Plug the extreme point

x = 0

into

5 - 2 x^{2} \Rightarrow y = 5

Maximum (0, 5)

Plug the extreme point

x = 2

into

5 - 2 x^{2} \Rightarrow y = - 3

Minimum (2, - 3)

Minimum (- 4, - 27), Maximum (0, 5), Minimum (2, - 3)

What is the extreme y=5-2x^2,-4<= x<= 2 ?
The extreme y=5-2x^2,-4<= x<= 2 is Minimum(-4,-27),Maximum(0,5),Minimum(2,-3)