Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Concavity of an integral function

  1. Sep 18, 2005 #1
    Hi guys,
    I am new in this forum and really hope that somebody can help me.
    I would like to show that the following function in concave of convex so I need to calculate the second derivative of Q(t) :

    Q(t)=Integral[upper=T; Lower=0]{tF(t)q(p-st)}dt
     
  2. jcsd
  3. Sep 19, 2005 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I assume you mean Q(T). t is just the "dummy" variable of integration.

    If [tex]Q(t)= \int_0^t (\tauF(\tau)q(p-s\tau))d\tau[/tex]
    then the best I can do is
    [tex]\frac{dQ}{dt}= tF(t)q(p-st)[/tex]
    (by the fundamental theorem of calculus) without knowing what F is. (And is q a constant or a function?)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Concavity of an integral function
Loading...