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!

Lagrange's mean value theorem problem

  1. Jan 31, 2015 #1
    1. The problem statement, all variables and given/known data
    New Doc 2_1.jpg

    2. Relevant equations

    Lagrange's mean value theorem
    3. The attempt at a solution
    Applying LMVT,
    There exists c belonging to (0,1) which satisfies f'(c) = f(1)-f(0)/1 = -f(0)
    But this gets me nowhere close to the options... :(
     
  2. jcsd
  3. Jan 31, 2015 #2

    O_o

    User Avatar

    edit
    Sorry the post I made contained an error. I'm not quite sure how to fix it yet but basically what I think you need to do is find a function h(x) and define it in terms of some linear combination of f(x), f(0), f(1) so that it equals zero at the end points and then apply Rolle's Theorem.
     
  4. Jan 31, 2015 #3
    Thanks mate!! Solved it... But how did you think of that function h(x)??
     
  5. Jan 31, 2015 #4
    But your h(x) had solved the problem. What was the error??
     
  6. Jan 31, 2015 #5

    O_o

    User Avatar

    Hey sorry I edited my previous post. What I wrote doesn't work because the two c's might be different. The c that works for the equation you posted might be a different c from the one I used for h(x).

    When trying to define an h(x) we want it to be 0 at the end points so we can apply Rolle's Theorem. It looks like Rolle's Theorem is needed because of the way the question is set up (i.e it looks like some derivative is equal to 0). And we want f(0) to disappear from the equation for the derivative because we don't know its value.
     
  7. Jan 31, 2015 #6

    O_o

    User Avatar

    Actually a relatively simple function works lol. Sorry for all this confusion:
    [tex]
    h(x) = xf(x)[/tex]
    There exists a c in (0, 1) such that [tex]
    0 = cf'(c) + f(c)[/tex]

    by Rolle's Theorem.
     
  8. Jan 31, 2015 #7
    Yah... Was just thinking the same and was about to post it... :P
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Lagrange's mean value theorem problem
Loading...