# Mean Value theorem question

1. Jun 22, 2011

### zeion

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

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.

2. Jun 22, 2011

### LCKurtz

The hypotheses are that a and b are real numbers and f is a function such that:

f(x) is continuous on [a,b]
f'(x) exists on (a,b)