Suppose you are grading a calculus project and a student submits the following answer to the question: Find the maximum of the function f(x) = x cos(x) on the interval [0, 3 ]. Is the answer correct? Give a full explanation.

• Student Answer: Since the cosine function is always between -1 and 1, the maximum value of the function f(x) = x cos(x) occurs when cos(x) = 1, i.e., when x = 2 .