This is a pretty tough question, so kudos to your academic program for teaching it to you. OK, relying only on Wikipedia, you attempted to find the correct function, in this case a titration curve, by estimating, and repeatedly determining the derivative.

Let's work with the titation of HCl and NaOH, that should be an easy to understand curve. What did you write as an approximate curve? And what curve did you determine experimentally?