What is the extreme f(x)=-x^2+6,-3<= x<= 4 ?

The extreme f(x)=-x^2+6,-3<= x<= 4 is Minimum(-3,-3),Maximum(0,6),Minimum(4,-10)

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extreme f(x)=-x^2+6,-3<= x<= 4

extreme

Minimum (- 3, - 3), Maximum (0, 6), Minimum (4, - 10)

Solution steps

Find the critical points:

x = - 3, x = 0, x = 4

Domain of

- x^{2} + 6, - 3 \leq x \leq 4 : - 3 \leq x \leq 4

Find intervals:

Increasing

: - 3 < x < 0,

Decreasing

: 0 < x < 4

Plug the extreme point

x = - 3

into

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

Minimum (- 3, - 3)

Plug the extreme point

x = 0

into

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

Maximum (0, 6)

Plug the extreme point

x = 4

into

- x^{2} + 6 \Rightarrow y = - 10

Minimum (4, - 10)

Minimum (- 3, - 3), Maximum (0, 6), Minimum (4, - 10)

What is the extreme f(x)=-x^2+6,-3<= x<= 4 ?
The extreme f(x)=-x^2+6,-3<= x<= 4 is Minimum(-3,-3),Maximum(0,6),Minimum(4,-10)