where xdata, ydata LPvalues:: vectors of the tpxk, yk quk0 datapoints the vector of values of Πn on the respective locations in xgrid n LPvalues must be computed using the Lagrange formulation Πnpxq ¸ y φ pxq, n k φkpxq k ¹ xx n j j 0 j k k 0 xkxj You may find the prod function useful here.( a) Consider the set of points tp1, 4q, p2, 3q, p3, 5q, p4, 7q, p5, 2qu. Use your LagrangePoly function to find the values of the interpolating polynomial on the grid 1:0.01:5. Plot on the same figure the datapoints with orange circles and the interpolating polynomial on the grid 1:0.01:5 with a solid line.( b) Repeat part( a) for the set of 11, 21, 31 uniformly distributed nodes xk in fRpxq 1 r1, 1s and ykfRpxk q, where 1 25x2 is Runge‘ s function on the grid-1:0.01:1. Use different colors when plotting the interpolating polynomials for each of the three cases and add a legend. Use ylim to show the plots for 1 ¤ y ¤ 1. Print on the screen a message for each case, stating the maximum absolute error between the function values and the interpolating polynomial values on the grid. 1 APMA0160, Spring 2017 Homework 5( c) Repeat part( b) for the set of 11, 21, 31 uniformly distributed nodes xk in rπ, πs and yk grid-pi: 0.01: pi.( d) Repeat part( b) for the set of 11, 21, 31 Chebyshev-Gauss-Lobatto nodes xk in on the grid-1:0.01:1. sinpxk q on the r1, 1s and ykfRpxk q( e) Write in a block of comments at the end of your prob1() function a few comments about the behavior