Results 1 to 2 of 2

Math Help - Convex functions

  1. #1
    Newbie
    Joined
    May 2012
    From
    .
    Posts
    3

    Convex functions

    Suppose f and g are two increasing convex functions on [0,1] with f(0) \leq g(0) and f(1)=g(1)=1. Show that
    (g'(x)-f'(x))(1-x) + g(x) - f(x) \geq 0.

    I know that f(x)+(1-x)f'(x) \leq 1, with the same for g. But that doesn't look that helpfull.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    May 2012
    From
    .
    Posts
    3

    Re: Convex functions

    I forgot to mention that f and g are polynomials with non-negative coefficients. I think it is sufficient that they are convex functions, but this maybe makes the problem easier?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Convex functions and increasing derivatives
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: November 10th 2010, 08:54 PM
  2. Convex Functions
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 9th 2010, 01:14 PM
  3. Sum of convex functions has a minimum
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: May 17th 2010, 01:39 PM
  4. convex functions
    Posted in the Calculus Forum
    Replies: 10
    Last Post: November 12th 2009, 02:19 PM
  5. Convex Functions
    Posted in the Calculus Forum
    Replies: 0
    Last Post: January 28th 2009, 02:25 PM

Search Tags


/mathhelpforum @mathhelpforum