1. Write a computer program to calculate the Lagrange interpolation polynomial P (x) to f(x) such that: n P(x)=f(x) j=0,1,2,......,n a) Apply it to some elementary functions or discrete data sets. b) Apply it to function f(x)=- 1 1+25x in the interval [-1,1] with equally spaced interpolation points and n=8, 16, 32. Plot P(x) and f(x) in [-1,1] interval to see the interpolation error. n+1 c) Do the same as in b, but use the roots of the Chebychev polynomial T, (x) as interpolation points. Compare results with those obtained in (b).