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

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

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

extreme points

f (x) = x^{2} - 4, - 2 \leq x \leq 3

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

Solution steps

Find the critical points:

x = - 2, x = 0, x = 3

Domain of

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

Find intervals:

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < 3

Plug the extreme point

x = - 2

into

x^{2} - 4 \Rightarrow y = 0

Maximum (- 2, 0)

Plug the extreme point

x = 0

into

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

Minimum (0, - 4)

Plug the extreme point

x = 3

into

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

Maximum (3, 5)

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

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