If f(x) is continuous on [0, 4] and f(0) = -3, f(4) = 5, which of the following must be true?
Correct: A
By the Intermediate Value Theorem, since f is continuous on [0, 4] and f(0) = -3 < 0 < 5 = f(4), there exists at least one c in (0, 4) such that f(c) = 0. Choice A is guaranteed. Choice B requires the Mean Value Theorem, which would require f to be differentiable, and we only know f is continuous. Choice C is true but is a weaker statement than A and not the 'must be true' that the question is targeting. Choice D is not guaranteed. The correct answer is A.