Find the critical numbers of the function

[phillyolly]

Homework Statement

Find the critical numbers of the function
y=√(1-x^2)

The Attempt at a Solution

y'=-x/√(1-x^2 )=0
-x/√(1-x^2 )=0

Here, I stuck. If I continue with this equation, my answers are x1=0 and x2 is less than 1.
But if I try to get rid of the root in order to find the critical points by doubling the both sides of equation, my answer is x1=0, x2 not equal to 1.

These are quite different answers. Please help me out with the problem.

 

[Mark44]

Homework Statement

Find the critical numbers of the function
y=√(1-x^2)

The Attempt at a Solution

y'=-x/√(1-x^2 )=0
-x/√(1-x^2 )=0

Here, I stuck. If I continue with this equation, my answers are x1=0 and x2 is less than 1.
But if I try to get rid of the root in order to find the critical points by doubling the both sides of equation, my answer is x1=0, x2 not equal to 1.

These are quite different answers. Please help me out with the problem.

Critical numbers occur at places where the derivative is 0, or at places in the domain of the function where the derivative is undefined, or at endpoints of the domain.

Seems to me that there are three critical numbers.

 

[phillyolly]

Critical numbers occur at places where the derivative is 0, or at places in the domain of the function where the derivative is undefined, or at endpoints of the domain.

Seems to me that there are three critical numbers.

Do you mean 0, 1, and -1?

x1=0

1-x^2=0 =>x=+-1

Is that what you mean?

 

[Mark44]

Yes, that's what I mean.