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

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

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

extreme

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

Solution steps

Find the critical points:

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

Domain of

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

Find intervals:

Decreasing

: - 2 < x < - 2,

Increasing

: - 2 < x < 2,

Decreasing

: 2 < x < 2

Plug the extreme point

x = - 2

into

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

Maximum (- 2, 0)

Plug the extreme point

x = - 2

into

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

Minimum (- 2, - 2)

Plug the extreme point

x = 2

into

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

Maximum (2, 2)

Plug the extreme point

x = 2

into

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

Minimum (2, 0)

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

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