I’m having trouble figuring out how to do the following problem. I’m not exactly sure what the teacher is trying ask us to do. I know what differences of y-values mean, but I’m just not sure how he wants us to go about it or this so called constant that we are looking for or levels of differences. This is a Pre-Calculus class.
You are given two polynomials, and a sequence of their values. You can take the sequence of differences, for example:
\begin{array}{r|rrrr} x&-3&-2&-1&0&1\\ \hline f(x)&0&14&16&12&8\\ \Delta f(x)&&14&2&-4&-4\\ \Delta^2f(x)&&&-12&-6&\ldots \end{array} Can you continue this table? And the same for the other polynomial? And how many more rows does it take until you reach a row that is constant?