Question

For f(x)=x^2/3(x^2-4) on [-2,2] the "c" value that satisfies the Rolle's Theorem is

A. 0
B. 2
C. +or-2
D. There is no value for c because f(0) does not exist
E. There is no value for c because f(x) is not differentiable on (-2,2)

Answer 1

f(-2) and f(2) do not exist.

Thus, the theorem's conditions are not satisfied -- f must be continuous on the closed interval.

This should have been clear, since none of the choices for c is in (-2,-2), except 0, and f(0) = 0.

However, D and E both give the wrong reason.

So, I pick
F. There is no value for c because f(x) is not continuous on [-2,2]