Question

Explain why Rolle's theorem does not apply to the function even though there exist a and b such that f(a) = f(b)?

1) The function is not continuous on the closed interval [a, b]
2) The function is not differentiable on the open interval (a, b)
3) The function does not satisfy the conditions of Rolle's theorem
4) The function is not defined on the interval [a, b]

Answer 1

Rolle's theorem does not apply to the function because it does not satisfy the conditions of the theorem.

Step-by-step explanation:

Rolle's theorem states that if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), and if the values of the function at the endpoints are the same, then there exists at least one point c in (a, b) where the derivative of the function is zero.

In this case, the given function does not satisfy the conditions of Rolle's theorem because it is either not continuous on the closed interval [a, b], or it is not differentiable on the open interval (a, b).

1. The function is not continuous on the closed interval [a, b].
2. The function is not differentiable on the open interval (a, b).
3. The function does not satisfy the conditions of Rolle's theorem.
4. The function is not defined on the interval [a, b].