Results 1 to 2 of 2

Math Help - differentiability of function g

  1. #1
    Junior Member
    Joined
    Dec 2011
    Posts
    57
    Thanks
    1

    differentiability of function g

    Suppose g is a function continuous on the closed and bounded interval
    [a, b], b > a > 0 and differentiable on the open interval (a, b).
    Prove that there exists a point β in (a, b) such that
    \frac{bg(a)-ag(b)}{b-a} = g(\beta) - \beta{g'(\beta).

    I tried to use the Mean Value Theorem, but I could not arrive at the answer.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member MathVideos's Avatar
    Joined
    Mar 2012
    From
    USA
    Posts
    37
    Thanks
    4

    Re: differentiability of function g

    Think about the mean value of g(x) and the mean value of g'(x). Remember, g'(x) has to, at one point, be equal to the average rate of change g(x)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. differentiability of function g
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: April 2nd 2012, 02:38 AM
  2. Even/odd function differentiability
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: March 24th 2010, 08:21 PM
  3. Test the differentiability of the function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 28th 2009, 12:50 PM
  4. Cauchy's function and differentiability
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: November 24th 2009, 10:57 PM
  5. Differentiability of the function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 6th 2008, 03:25 AM

Search Tags


/mathhelpforum @mathhelpforum