Suppose that f(x) and g(x) are differentiable functions on the interval [a, b]. The Intermediate Value Theorem states that if f(a) < 0 and f(b) > 0, or f(a) > 0 and f(b) < 0, then which of the following must be true?

Core Concept

This question tests the student's understanding of the Intermediate Value Theorem. This theorem states that if a function is continuous and takes on both positive and negative values at two points, then it must take on 0 at some point between those two points. Option B is incorrect because the theorem does not guarantee that f(x) > 0 for some x ∈ (a, b). Option C is incorrect because the theorem does not guarantee continuity of the derivative. Option D is incorrect because differentiability is not guaranteed by the theorem.