1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Problem Mean value theorem
Loading...