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Homework Help: Problem Mean value theorem

  1. Nov 2, 2009 #1
    1. The problem statement, all variables and given/known data
    http://img14.imageshack.us/img14/6132/proiqc.jpg [Broken]

    2. Relevant equations

    3. The attempt at a solution
    the first 3 are from the textbook so they must be right.. the last 2 im pretty sure i got right too..
    because the 4th one, if f'(x)=0 then f(x)= c .. so its false.
    im not too sure about the 5th one but im 90% sure it should true.
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Nov 2, 2009 #2
    (1) is Rolle's Theorem (Edit: this is incorrect - see the following posts)
    (2) is the Mean Value Theorem, which is a generalization of Rolle's Theorem
    I did not know (3) but that is interesting
    (4) is correct, f(x) can be a constant function not equal to 0.
    (5) is correct - take a(x) = f(x) - g(x). It's derivative is 0, so a(x) is constant (you can prove this using MVT).
    Last edited: Nov 3, 2009
  4. Nov 2, 2009 #3
    i know that 1 and 2 are Rolle's Theorem and Mean Value Theorem, and its written exactly like in my textbook.. i cant find the mistake.

    https://www.physicsforums.com/library.php?do=view_item&itemid=231 its even stated here..

    so what is wrong?
  5. Nov 2, 2009 #4
    Oh sorry, I missed that
    (1) states that f is defined on [a,b] but it is not necessarily continuous there. It is continuous on (a,b) (since it is differentiable there) but not necessarily at a or b.
  6. Nov 2, 2009 #5
    thats a tricky question.. weird.
    thanks a lot for your help man!
  7. Nov 3, 2009 #6
    No problem, can't believe I missed that
    In my experience, the physical science courses are where they try to 'trick' you like that, I've never had any questions like that when I was a math undergrad. I guess now you've learned that you have to pay attention to every little detail when writing tests in this class (which is probably a good idea, regardless). Cheers.
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