I want to create problems concerning polynomial interpolation for students. However, I need those problems to differ in difficulty for the different students.
What I could always do is solve some problem and classify them by difficulty. However, it would be nice if I could find a "system" with I could create such problems. This would also have the benefit that the problems for the students do not repeat themselves (most of the time).
The students are supposed to either use the classic approach, the newton approach, or the lagrange approach. Each one of them needs to be understood.
Is there a way to create such problems? and where in the process would I be able to increase / decrease difficulty?
The problems btw only ought to consist of the data points, from which the polynomial has to be interpolated.
I already tried building relatively easy polynomials and then calculating the data points for the problem, however calculation would still get complicated for the students. Nice, clean and easy numbers would be great. Numbers like 1/4, 1/2, 1/5 etc. would also be fine. I just want to avoid the students having to work with numbers such as 83.23461.
Thank you in advance.