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

The extreme g(x)=xsqrt(2-x^2) is Maximum(-sqrt(2),0),Minimum(-1,-1),Maximum(1,1),Minimum(sqrt(2),0)

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extreme g(x)=xsqrt(2-x^2)

extreme

Maximum (- 2, 0), Minimum (- 1, - 1), Maximum (1, 1), Minimum (2, 0)

Solution steps

Find the critical points:

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

Domain of

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

Find intervals:

Decreasing

: - 2 < x < - 1,

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < 2

Plug the extreme point

x = - 2

into

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

Maximum (- 2, 0)

Plug the extreme point

x = - 1

into

x 2 - x^{2} \Rightarrow y = - 1

Minimum (- 1, - 1)

Plug the extreme point

x = 1

into

x 2 - x^{2} \Rightarrow y = 1

Maximum (1, 1)

Plug the extreme point

x = 2

into

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

Minimum (2, 0)

Maximum (- 2, 0), Minimum (- 1, - 1), Maximum (1, 1), Minimum (2, 0)

What is the extreme g(x)=xsqrt(2-x^2) ?
The extreme g(x)=xsqrt(2-x^2) is Maximum(-sqrt(2),0),Minimum(-1,-1),Maximum(1,1),Minimum(sqrt(2),0)