Hi, I'm new here and I'm not sure if this is the right section or not if it is in the wrong section please let me know and I'll post it there instead.
I have been racking my brain with this for a couple days and am embarrassed that I can't figure it out (at one point I considered myself good at this kind of thing)... Just so you know this is NOT Homework, but a personal project of mine that I have been working on. The field is economics and expenditure models.
I am looking for a f(x) that can be determined given a set of knowns at two different points:
@ x1, f(x1) and f '(x1) are know and
@ x2, f(x2) and f '(x2) are also known
relationship between the two points -- x2>x1, f(x2)>f(x1), f '(x2)<f '(x1)
My though was to use a function in the form of f(x) = A logb(x) - C, but I could not get it to work.