1. Consider the following data, which are obtained from a smooth function also known as Runge's function, y = (1+25x2): X 1.00 -0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00 10.038 0.058 0.100 0.200 0.500 1.00 0.500 0.200 0.100 0.058 0.038 The Lagrange polynomial interpolation, for which the value at any point x is simply x-xt P(x) = y; n7 1=0 1=6*; --X Write a computer program for Lagrange interpolation. Test your program by verifying that P(0.7)=-0.226. (a) Using the above data in the table, find the interpolated value at x=0.9. (10 pts) (b) Use Runge's function to generate a table of 21 equally spaced data points. Interpolate these data using a Lagrange polynomial of order 20. Plot this polynomial and comment on the comparison between your result and the plot of part (a). (10 pts)