Let f(x)=1+x21

Interpolate f(x) on the interval [-5,5] with Lagrange polynomials of degree n, P_n(x), which agree with f at n+1 equally spaced points on the interval. Do this for n=5, 10, 15, 20. Explain what method you are using to compute the polynomials. You may use matlab commands polyval and polyfit.

Plot P₅(x), P₁₀(x), and P₁₅(x) separately, but with each f(x). (When displaying a graph, plot the points x_i,y_i where x_i-x_i-1 = 0.01)

Compute the error at the point q=1+(10) for each of the approximations. What would you expect to happen as n gets larger? What is actually happening?