Question

Can Rolle's theorem be applied to f on the closed interval [a, b]?

1) Yes
2) No
3) Cannot be determined

Answer 1

Rolle's theorem cannot be applied to the closed interval [a, b] because it requires the function to be differentiable in the open interval.

Step-by-step explanation:

In order to apply Rolle's theorem, the function f must be continuous on the closed interval [a, b] and differentiable on the open interval (a, b). It is important to note that Rolle's theorem states that if a function satisfies these conditions and f(a) = f(b), then there exists at least one point c in the open interval (a, b) where the derivative of the function is zero.

Therefore, Rolle's theorem cannot be applied to the closed interval [a, b] as it requires the function to be differentiable in the open interval.