A function f(x) is continuous on the interval [0, 4] and has a local maximum at x = 2. Which of the following conclusions can be drawn about the function f(x) on the interval [0, 4]?

Core Concept

A local maximum at x = 2 means that the function has a value greater than the values of the function at nearby points. However, this also means that the function has a jump discontinuity at x = 2, since the function values on either side of x = 2 must be different (otherwise, there wouldn't be a local maximum at x = 2). The correct answer is D) The function has a jump discontinuity at x = 2. Options A, B, and C are incorrect because the function does not have a global maximum at x = 2, the function does not have a local minimum at x = 4, and the function does not have a removable discontinuity at x = 0.