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
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