What is the domain of the function f ?
Rolle's theorem doesn't apply because the function is not continuous on [-2, 0]. (There is a discontinuity at x = -1.)
a) I already said why this is true.
b) f(-2) does equal f(0).
and
c) f(x) is, in fact, not differentiable at x = -1 because the function does not exist there.
As both a) and c) are true, and Rolle's theorem depends on them being true (and f(-2) = f(0) to boot) the answer should be d).
-Dan