Rolle's Theorem

Continuity: Continuity refers to whether or not there are any breaks or jumps in a function. For Rolle's theorem to apply, it requires continuity on the closed interval [a, b].

Differentiability: A function is differentiable if it has a derivative at every point in its domain. Rolle's theorem requires the function to be differentiable on the open interval (a, b).

Extreme Value Theorem: The Extreme Value Theorem states that if a function is continuous on a closed interval [a, b], then it must have both a maximum and minimum value within that interval.