Study of a real function
- To: mathgroup at smc.vnet.net
- Subject: [mg123431] Study of a real function
- From: Vicent <vginer at gmail.com>
- Date: Wed, 7 Dec 2011 06:14:12 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
Hello.
This is an "old" question ,but I would like to ask it here again in order
to get your suggestions. I would appreciate any kind of help.
I am interested in studying a one-variable real function called F(x). In
fact, I want to PROVE what I can see when I plot it: it has only one
maximum and it decreases as "x" goes to infinity, and it also decreases if
"x" decreases ("x" ranges from 2 to infinity).
The problem is that the definition or expression for F depends on some
integer parameters. So, in fact, I don't have a single function F but a
"set" or "class" or "collection" of functions F with the same structure. By
plotting them it seems to me that in ALL possible cases F will have the
same behavior I want to prove, but obviously the maximum depends on the
values of the integer parameters I just mentioned. And I want to PROVE it
for the general case, of course.
I got the analytic expression for the first derivative of F by using this:
derivF[p1_, p2_, x_] = D[F[p1, p2, x], x]
where p1 and p2 stand for those integer parameters I mentioned.
I tried to look for maximums and/or mimimums of F by solving The
function derivF
derivF ==0, but derivF seems to be too complex for the Mathematica command
Solve.
I also tried to do something like this: Reduce[F[parameters, x] <= 0,
lambda], but it is still "Running...".
So... What would you recommend me to do? F is a "strange" but still
continuous function. It involves the use of the function "Erfc".
Thank you in advance for your suggestions.
--
vicent
dooid.com/vicent
- Follow-Ups:
- Re: Study of a real function
- From: DrMajorBob <btreat1@austin.rr.com>
- Re: Study of a real function