Question

Find the critical numbers of the function.
g(x) = square root of (1 − x^2)

Answer 1

You can get the y and x intercepts and maximum y value either through algebra or with differential calculus. Which do you prefer?

Answer 2

I'm in calculus

Answer 3

Max can be gotten through algebra by completing the square method. Calculus by differentiating and setting the first derivative to 0 and either 1) seeing whether the slope of the derivative goes from + to - or - to + or 2) taking the second derivative to see if the curve is concave up or down. Just got your post and see that you want calculus. Okay.

Answer 4

Can you calculate the first derivative or do you need help with that part?

Answer 5

If you can help that would be great. I'm not great with derivatives.

Answer 6

Okay, keeping with the spirit of this site, I'm going to give you some formulas to work instead of just handing out an answer. Your equation is a polynomial which you can break up into terms and take the derivative of each term and add them. The first term is "1" which is a constant and the derivative of a constant is 0, so just look at the second term. if y = ax^n, then y' = anx^(n-1). Show your work.

Answer 7

Do you know the chain rule?

Answer 8

yes

Answer 9

y' = [(1/2)(1 - x^2)^(-1/2)](-2x). Do you see how I got that? Still needs a little simplifying.

Answer 10

Yeah, I see where I went wrong now thought. I forgot the -2x

Answer 11

So, y' = -x(1 - x^2)^(-1/2). Okay, you say you see now where you went wrong. Are you all set now or need further help?

Answer 12

I think I've got it now, thank you!

Answer 13

Good luck to you on all your studies!