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!

Cauchy theorim question

  1. Jan 20, 2009 #1
    i got this question

    here is the solution:
    they are taking the minimal value
    and the maximal value
    the innequalitty that the write is correct min< <max

    but why??
  2. jcsd
  3. Jan 20, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    Well, if you have
    [tex]f(x_1) + f(x_2) + \cdots + f(x_n)[/tex]
    and you know that each of the [itex]f(x_i)[/itex] is not greater than M, then you can write
    [tex]f(x_1) + f(x_2) + \cdots + f(x_n) \le M + M + \cdots + M = n \cdot M;[/tex]
    similarly for the minimum.

    It's simply applying the inequality that
    x + y <= M + y
    if x <= M.
  4. Jan 20, 2009 #3
    i agree with you
    but why they do that
    how is it linked to cauchy theorem
  5. Jan 20, 2009 #4


    User Avatar
    Science Advisor
    Homework Helper

    I don't know what it has to do with Cauchy's theorem, but it does have to do with the intermediate value theorem: for any value c between m and M (assuming some conditions on f which you didn't state) there is an x such that f(x) = c.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Cauchy theorim question
  1. Mean theorim question (Replies: 9)