What is the extreme f(x)=sqrt(-x^2+1),-1<= x<= 0 ?

The extreme f(x)=sqrt(-x^2+1),-1<= x<= 0 is Minimum(-1,0),Maximum(0,1)

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extreme f(x)=sqrt(-x^2+1),-1<= x<= 0

extreme

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

Solution steps

Find the critical points:

x = - 1, x = 0

Domain of

- x^{2} + 1, - 1 \leq x \leq 0 : - 1 \leq x \leq 0

Find intervals:

Increasing

: - 1 < x < 0

Plug the extreme point

x = - 1

into

- x^{2} + 1 \Rightarrow y = 0

Minimum (- 1, 0)

Plug the extreme point

x = 0

into

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

Maximum (0, 1)

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

What is the extreme f(x)=sqrt(-x^2+1),-1<= x<= 0 ?
The extreme f(x)=sqrt(-x^2+1),-1<= x<= 0 is Minimum(-1,0),Maximum(0,1)