Computer science people, I am looking to be pointed in the right direction. I am looking for a solution to a problem, and I think the answer might lie in an area of Computer Science/Statistics/O.R. that I know very little about. Here's the deal:
I have two mathematical functions, f_1 and f_2. Both functions intersect with the Y axis at exactly two points (and basically what happens below the Y axis can be ignored). f_1 is fixed; it's input. But f_2 is defined in terms of two parameters that I can tweak. Here's what I am trying to answer:
How can I pick the two parameters of f_2 so that the area under f_2 is as large as possible and yet still contained entirely within the area under f_1?
I have come up with sort of a brute-force algorithm that I think will solve the problem, but if there's a 'best' or well-known way to solve this class of problems I'd like to learn more about it. I have heard about topics like 'function optimization.' Is this relevant? Also, because what I am doing is sort of a surprise, I'd like to hide most of the details, but I can give more if that will help the quality of your responses.