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

The extreme f(x)=-x^2+2x+4,-2<= x<= 4 is Minimum(-2,-4),Maximum(1,5),Minimum(4,-4)

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

extreme

Minimum (- 2, - 4), Maximum (1, 5), Minimum (4, - 4)

Solution steps

Find the critical points:

x = - 2, x = 1, x = 4

Domain of

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

Find intervals:

Increasing

: - 2 < x < 1,

Decreasing

: 1 < x < 4

Plug the extreme point

x = - 2

into

- x^{2} + 2 x + 4 \Rightarrow y = - 4

Minimum (- 2, - 4)

Plug the extreme point

x = 1

into

- x^{2} + 2 x + 4 \Rightarrow y = 5

Maximum (1, 5)

Plug the extreme point

x = 4

into

- x^{2} + 2 x + 4 \Rightarrow y = - 4

Minimum (4, - 4)

Minimum (- 2, - 4), Maximum (1, 5), Minimum (4, - 4)

What is the extreme f(x)=-x^2+2x+4,-2<= x<= 4 ?
The extreme f(x)=-x^2+2x+4,-2<= x<= 4 is Minimum(-2,-4),Maximum(1,5),Minimum(4,-4)