Explain why Rolle's Theorem does not apply to the function even though there exist a and b such that f(a) = f(b). (Select all that apply.)

Question

1. f '(a) does not equal f '(b) for any values in the interval [-1, 1].
2. There are points on the interval [a, b] where f is not continuous.
3. There are points on the interval (a, b) where f is not differentiable.
4. None of these.
5. f(a) does not equal f(b) for all possible values of a and b in the interval [-1, 1].

Answer 1

f'(x) does does not exist at x=0 which is in the interval[-1,1]

and Rolle's requires it does to be certain true

f'(x)=(3/2)(2-x^2/3)^1/2*(-2/3)x^-1/3

x^-1/3=1/x^1/3 which has no value at x=0