Results 1 to 2 of 2

Math Help - Derivative Problem

  1. #1
    Junior Member
    Joined
    Mar 2010
    Posts
    62

    Derivative Problem

    Let f and g be functions with continuous second derivatives on [0,1] and f^{'}(0)g^{''}(0)-f^{''}(0)g^{'}(0) \neq 0. Define a function \theta for x \in (0,1) so that \theta (x) is one of the values that satisfies the generalised mean value theorem,
    \frac{f(x)-f(0)}{g(x)-g(0)} = \frac{f^{'}(\theta (x))}{g^{'}(\theta (x))}.
    Show that
    \lim_{x \to 0^+} \frac{\theta (x)}{x} = \frac{1}{2}.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Mar 2010
    Posts
    62
    Hey so has anyone managed to solve this?

    The hint given is that differentiate each side of
    [f(x)-f(0)]g^{'}(\theta (x)) = [g(x)-g(0)]f^{'}(\theta (x))
    with respect to x, collect the terms that involve \theta ^{'}(x) on one side, divide both sides by x, and then take the limit of each side as x \rightarrow 0^{+}.

    Despite the hint, I'm still stuck. Is there anyone who can help? Thanks.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Derivative Problem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 21st 2010, 06:22 PM
  2. derivative problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 22nd 2010, 07:27 PM
  3. derivative.. problem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: January 27th 2010, 02:16 PM
  4. derivative problem -
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 2nd 2008, 11:09 AM
  5. Derivative problem
    Posted in the Calculus Forum
    Replies: 6
    Last Post: September 17th 2008, 06:39 PM

Search Tags


/mathhelpforum @mathhelpforum