The Intermediate Value Theorem states that if a function f(x) is continuous on the interval [a, b] and k is any value between f(a) and f(b), then there exists a value c in the interval [a, b] such that f(c) = k. Which of the following conclusions can be drawn about the function f(x) = sin(x) on the interval [0, π]?

Core Concept

The function f(x) = sin(x) is continuous on the interval [0, π] because it is differentiable on this interval. Additionally, sin(0) = 0 and sin(π) = 0, so the function takes on the value 0 at both endpoints of the interval. By the Intermediate Value Theorem, there exists a value c in the interval [0, π] such that sin(c) = 0. The correct answer is A) The function is continuous on the interval [0, π]. Options B, C, and D are incorrect because the function is not discontinuous on this interval, and the local maximum and minimum statements are not accurate.