Suppose that f(x) is a continuous function on the interval [a, b] and f(a) = f(b). Determine which choice best describes the following statement?
1) The function f(x) has a local maximum at some point in the interval (a, b).
2) The function f(x) has a local minimum at some point in the interval (a, b).
3) The function f(x) is constant on the interval [a, b].
4) The function f(x) is increasing on the interval [a, b].
5) The function f(x) is decreasing on the interval [a, b].