[35 pts.] A car travelling along a straight road is clocked at a number of points. The data from the observations are given in the following table, where the time is in seconds, the distance is in feet, and the speed is in feet per second. Time xi Distance vi 0 Speed si 6 374 80 10 643 75 13 982 73 0 220 76 74 (a) Write a MATLAB function a-HermiteInterp(x.y,s) which use Newton's divided difference to compute the Hermite polynomial interpolating given data {(xi ,yi,si)} n i=1. (b) Write a MATLAB function pval-HornerHermite(ax,t) which evaluate Hermite polynomials at given points t by using Horner's rule. (c) Use your MATLAB functions in (a) and (b) to compute the Hermite polynomial for the data in the table and predict the position of the car att-8 s. (d) Use the derivative of the Hermite polynomial to predict the speed of the car att = 8 s. (You may compute the derivative by using MATLAB build-in functions diff and subs. Type help sym/diff and help subs in MATLAB main command window to see how to use them.) [35 pts.] A car travelling along a straight road is clocked at a number of points. The data from the observations are given in the following table, where the time is in seconds, the distance is in feet, and the speed is in feet per second. Time xi Distance vi 0 Speed si 6 374 80 10 643 75 13 982 73 0 220 76 74 (a) Write a MATLAB function a-HermiteInterp(x.y,s) which use Newton's divided difference to compute the Hermite polynomial interpolating given data {(xi ,yi,si)} n i=1. (b) Write a MATLAB function pval-HornerHermite(ax,t) which evaluate Hermite polynomials at given points t by using Horner's rule. (c) Use your MATLAB functions in (a) and (b) to compute the Hermite polynomial for the data in the table and predict the position of the car att-8 s. (d) Use the derivative of the Hermite polynomial to predict the speed of the car att = 8 s. (You may compute the derivative by using MATLAB build-in functions diff and subs. Type help sym/diff and help subs in MATLAB main command window to see how to use them.)