Results 1 to 2 of 2

Math Help - Lagrange's Theorem(?)

  1. #1
    Member
    Joined
    Aug 2009
    From
    Mumbai
    Posts
    83

    Lagrange's Theorem(?)

    Given two positive real numbers , prove that

    \sqrt{ab}<[(a-b)/(\ln(a)-\ln(b))]<(a+b)/2

    One thing that strikes me first is that the middle term is actually the point in (a,b) which satisfies Lagrange's Mean Value Theorem for the function \ln(x)

    But I can't think of any way of proving that the point lies between the geometric mean and the arithmetic mean of the numbers a,b.

    Any suggestions??
    Last edited by bandedkrait; January 10th 2010 at 11:17 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Jan 2010
    Posts
    3

    maybe you can consider this

    let f(x)=\frac{x-a}{lnx-lna}-\sqrt{ax}, then see f'(x) and f''(x).

    another possible way: through Taylor's Mean Value Theorem. But I have not tried it.
    Last edited by Fresnel; January 14th 2010 at 02:38 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove Wilson's theorem by Lagrange's theorem
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: April 10th 2010, 02:07 PM
  2. Lagrange's Theorem
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: September 24th 2009, 01:46 PM
  3. Lagrange's Mean Value Theorem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 20th 2008, 07:31 AM
  4. Lagrange Theorem.
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 16th 2008, 08:04 PM
  5. Lagrange Theorem etc.
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 1st 2008, 01:50 AM

Search Tags


/mathhelpforum @mathhelpforum