Home Tools assignment-5.pdf x assignment-4.pdf Sustainable and... Presentation title... Kincaid D , Chene... Sign In T 1 12 188% Share Po Jacobs University Bremen Spring Semester 2020 Prof. Preusser Numerical Methods I Assignment Sheet 5. Due: March 11, 2020 Exercise 21 [3 + 4 + 4 + 4 Points]: Consider function the function f (ac) =- 4x2 + 1 a) Derive the polynomial p1(x) in Newton form that interpolates f(x) by taking 5 equally spaced nodes across the interval [-1, 1], i.e. taking nodes -1, -1/2, 0, 1/2, 1. b) Calculate the interpolation error maxxEl-1,1] If (x) - P1(x) | of the solution in a). c) Re-compute the steps in part a) when using 5 Chebyshev nodes to compute the polynomial p2(x) in Newton form. d) Calculate the interpolation error maxxe[-1,1] If (x) - p2(x)|