# Concavity of an integral function

1. Sep 18, 2005

### gohou@econ.umd.edu

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. Sep 19, 2005

### HallsofIvy

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

If $$Q(t)= \int_0^t (\tauF(\tau)q(p-s\tau))d\tau$$
then the best I can do is
$$\frac{dQ}{dt}= tF(t)q(p-st)$$
(by the fundamental theorem of calculus) without knowing what F is. (And is q a constant or a function?)