Question

If you were to use the method of undetermined coefficients to find a polynomial function whose graph passes through five given points, what would be the largest possible degree of the polynomial? Explain your reasoning

Answer 1

I think that with undetermined coefficients the functions have to be linearly independent right? In any event I really couldn't guess, because you could just as well have 5 points that work for even a sin(t) so as long as they are all on there. I wouldn't just say that a polynomial ^6, would be the highest even though I know it is going to have multiple inflection points. It is hard to say, but I'm pretty sure they are all independent of each other in that method. I have only used it in diff eq, for solving an implicit solution for a diff eq, and there I had something to go by.