(2) In this question you construct (without the use of code; you may use a calculator, though) a polynomial interpolant to data via the divided differences approach. You then evaluate your polynomial and its first derivative using nested multiplication. (a) Add four data points of your own choice to the given point (1,2), and construct a divided difference table corresponding to these five points. Do not use the number 4 and -1 as interpo- lation points. Using the table, find the polynomial in 114 that interpolates your data. Write that polynomial in two different Newton forms. (b) Using nested multiplication evaluate each of the above forms at x = 4 and x = -1. Now, use nested multiplication in order to evaluate the derivative of each form at x = 4 (note that you are double checking yourself, since the two forms represent the same polynomial). (c) Now replace one of your points by the point (3,2), and find the new polynomial interpolant. You are free to choose which point to delete, but you want to be efficient here, hence you wish to use the output of (a) to the extent that this is possible. Choose the point to be deleted in a way that minimizes the additional computations, and find the new polynomial that interpolates the new dataset