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Mean Value theorem question

  1. Jun 22, 2011 #1
    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.
     
  2. jcsd
  3. Jun 22, 2011 #2

    LCKurtz

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    Science Advisor
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    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)

    Does that help you think through your question?
     
  4. Jun 22, 2011 #3
    Yeah I think you just answered my question.
     
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