Let f be a function that is continuous on the closed interval [1, 5] and differentiable on the open interval (1, 5). If f(1) = 3 and f(5) = 11, which of the following must be true?

Core Concept

By the Mean Value Theorem, since f is continuous on [1, 5] and differentiable on (1, 5), there exists some c in (1, 5) such that f'(c) = (f(5) - f(1))/(5 - 1) = (11 - 3)/(5 - 1) = 8/4 = 2.