Suppose that f(x) is a twice-differentiable function defined on the closed interval [a, b]. If f'(c) = 0 for a < c < b, which of the following must be true?
1) f(x) has a local maximum or minimum at x = c
2) f(x) has a point of inflection at x = c
3) f(x) is increasing on the interval [a, c] and decreasing on the interval [c, b]
4) f(x) is decreasing on the interval [a, c] and increasing on the interval [c, b]