Question

How do you determine whether Rolle's theorem can be applied to `f(x) = (x^2 - 1) / x` on the closed interval [-1,1]?

Answer 1

Rolles theorem states: "Let f be continuous on a closed interval [a, b] and differentiable on the open interval (a, b). If f(a) = f(b), then there is at least one point c in (a, b) where f '(c) = 0."

Explanation:

The first criteria is NOT met. Specifically, f is NOT continuous on the interval [-1, 1] at the point x = 0.

At x = 0, the function is undefined.

Hope that helps.