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

Answer 1

Roles theorem states that if you have two points \(x_1\) and \(x_2\) where the function is equal \(f(x_1) = f(x_2)\), then somewhere on that interval \(c \in [x_1, x_2]\) it must be the case that the derivative is 0 \(f'(c) = 0\)... If I recall correctly.

So my advice is to find an interval where the endpoints have the same endpoint.
For example, does \(f(0) = f(3)\)?

Answer 2

endpoints have the same function output, I mean.

Answer 3

Another condition is that the interval is continuous.