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21 DATE 5.2 Concepts Worksheet NAME Theorems of Calculus Rolle's Theorem states: If a function is continuous at every point on a closed interval [a, b] and differentiable on every point of its interior (a, b) and f(a) = f(b) = 0, then there is at least one number c between a and b at which f'(c) = 0. A variation of Rolle's Theorem includes broader conditions: If a function f(x) is continuous at every point in a closed interval [a, b] and f(a) = f(b), then there exists at least one critical point of f(x) between x = a and x = b. 1. Using this variation of Rolle's Theorem, find and mark the critical points on the following graphs, if applicable. If not applicable, explain why not. (a) (b) (c) (d) W