What is the extreme f(x)=sqrt((4-x^2)^2) ?

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

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extreme f(x)=sqrt((4-x^2)^2)

extreme points

f (x) = (4 - x^{2})^{2}

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

Solution steps

Find the critical points:

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

Domain of

(4 - x^{2})^{2} : - \infty < x < \infty

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug the extreme point

x = - 2

into

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

Minimum (- 2, 0)

Plug the extreme point

x = 0

into

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

Maximum (0, 4)

Plug the extreme point

x = 2

into

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

Minimum (2, 0)

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

3 x + 2 y

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