Use the graph of f(x)=x^2/(x^2-4) to determine on which of the following intervals Rolle’s Theorem applies.

Question

Use the graph of f(x)=x^2/(x^2-4) to determine on which of the following intervals Rolle’s Theorem applies. 
A. [0, 3]
B. [-3, 3]
C. [-3/2, 3/2]
D. [-2, 2]
E. none of these
 
I know what the Rolle's Theorem is but I'm unsure on how you know if the function is continuous and differentiable. The domain I think is all except -2 and 2 so how would that affect the differentiable side. I have eliminated choice A because f(0) and f(3) do not equal each other.

I'm just confused.

Steve · Answer

Since f(x) is not defined for x = ±2, any interval which includes either of those values will not satisfy the theorem.

So, A,B,D are all out

The only possible choice is C, which is ok, because f(-3/2) = f(3/2)