The function f(x) = x(64-x^2)^1/2 satisfies the hypotheses of Rolle's Theorem on the interval [-8,8]. Find all values of that satisfy the conclusion of the theorem.
a.) + 1, AND -1
b.) + 4sqrt(2) and -4sqrt(2)
c.) 4sqrt(2)
d.) 1
My answer. The intervals do match and equal zero so Rolles theorem can work.
Second I found the derivative maybe thats where I can't solve this problem.
The derivative that I got was 64-x^2+x/sqrt(64-x^2) maybe i did wrong on the simplifying. I at least tried hopefully some one can explain as much as possible with every single step because I can figure out the algebra part.