What is the extreme f(x)=x^2+4x+4,-4<= x<= 0 ?

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

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extreme f(x)=x^2+4x+4,-4<= x<= 0

extreme points

f (x) = x^{2} + 4 x + 4, - 4 \leq x \leq 0

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

Solution steps

Find the critical points:

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

Domain of

x^{2} + 4 x + 4, - 4 \leq x \leq 0 : - 4 \leq x \leq 0

Find intervals:

Decreasing

: - 4 < x < - 2,

Increasing

: - 2 < x < 0

Plug the extreme point

x = - 4

into

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

Maximum (- 4, 4)

Plug the extreme point

x = - 2

into

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

Minimum (- 2, 0)

Plug the extreme point

x = 0

into

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

Maximum (0, 4)

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

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