Concavity of an integral function

  • #1

Main Question or Discussion Point

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
 

Answers and Replies

  • #2
HallsofIvy
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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?)
 
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