Results 1 to 8 of 8

Math Help - Obtaining the maximum of a shifted function

  1. #1
    Newbie
    Joined
    Jun 2010
    Posts
    3

    Obtaining the maximum of a shifted function

    I have a continuous function f(x) , whose maximum Fm occuring at x=Xo is known.

    Can we find the maximum of g(x) = f(x+A) + f(x-A) from the above information and the value of x where we have the maximum of g(x) ?

    Is there any way to do this please let me know.

    Thanks & Regards
    Anindya
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Is f differentiable? Over what interval are you maximizing the function? Does the maximum of f that you know occur at a critical point, or at an endpoint of your interval of interest?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2010
    Posts
    3
    Yes F is differentiable . Sorry i forgot to add that. The maximum of f occurs at a critical point
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    May 2010
    Posts
    1,028
    Thanks
    28
    except in trivial cases (eg A=0), i dont think you can do this from the information provided. Do you have any more information about f(x)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jun 2010
    Posts
    3
    No i don't.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Ok, f differentiable implies g is differentiable. The derivative of g is

    g'(x)=f'(x+A)+f'(x-A).

    As SpringFan25 has noted, setting g'(x)=0 is a bit problematic. I'm not exactly sure how you would go about solving that. You know that f'(x_{0})=0. But I'm not seeing where you would go next. For, if you set x+A=x_{0}, then x=x_{0}-A, and x-A=x_{0}-2A. Then what? You don't know that the second term is zero.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Nov 2009
    Posts
    130
    Use the definition of derivative... Just and idea...
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member mfetch22's Avatar
    Joined
    Feb 2010
    From
    Columbus, Ohio, USA
    Posts
    168
    Quote Originally Posted by Anindya View Post
    I have a continuous function f(x) , whose maximum Fm occuring at x=Xo is known.

    Can we find the maximum of g(x) = f(x+A) + f(x-A) from the above information and the value of x where we have the maximum of g(x) ?

    Is there any way to do this please let me know.

    Thanks & Regards
    Anindya
    I know that the maximum of the function f(x+A) is x=Xo-A, and that the maximum of the function f(x-A) is x=Xo+A, but I'm not sure how to do it when the functions are added together. I'm not sure where to go on this one, like the previous poster said, is there anymore information about f(x)? I hope the facts above about the sperate functions help, otherwise I've just wasted space.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Shifted Legendre Polynomial
    Posted in the Advanced Math Topics Forum
    Replies: 3
    Last Post: October 24th 2010, 07:32 AM
  2. Replies: 0
    Last Post: September 10th 2010, 08:53 AM
  3. Shifted fcn...
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 30th 2010, 10:15 PM
  4. Shifted Riemann
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 15th 2009, 03:33 PM
  5. Shifted exponential
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: February 18th 2009, 05:19 PM

Search Tags


/mathhelpforum @mathhelpforum