Problem 15. Consider the following data tables: (11}: 2 8 35:,11 l 4 5 (III) 6 0 2 x I D 8 2 4 {IV} 3: 22 ID I] -14 [a] Find the Lagrange form of the interpolating polynomial for each data set. [b] Find the Newton form of the interpolating polynomial for each data set. [0] Verify that your answers to {a} and {b} simplify to the same polynomial. (d) Add the point (3, 1} to each data table above. and nd the interpolation polynomial for the modied data sets