Originally Posted by

**Skrymir** 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:

@ x_{1}, f(x_{1}) and f '(x_{1}) are know and

@ x_{2}, f(x_{2}) and f '(x_{2}) are also known

relationship between the two points -- x_{2}>x_{1}, f(x_{2})>f(x_{1}), f '(x_{2})<f '(x_{1})