1. The problem statement, all variables and given/known data What set(s) are a and b assumed to be elements of? Does the mean Value Theorem make a universal claim (for all a ... for all b) or an existential claim (there exists a ... there exists b) about a and b? Explain how you came to this conclusion. 2. Relevant equations We were told to look at the wikipedia page: http://en.wikipedia.org/wiki/Mean_value_theorem 3. The attempt at a solution Initially I thought that a and b are assumed to be elements of the domain of the function in question... so assumed that f(x) fulfills the antecedent of the theorem, then for every a, b in the domain of f(x) the consequent is true. But then can I also assume that a and b are all elements of the real numbers, then for every function that happens to be continuous on this interval, the consequent is true? Does that matter? Am I confusing myself? lol.