On the interval [-1,1], consider interpolating Runge’s functionf(x) = 1/ (1 + 25x^2) By Pn(x), use computer to graph:
(c) Take 11 equally spaced nodes in [-1,1], starting at –1,ending at 1, and obtain the interpolating polynomial P10(x). Also,use 11 Chebyshev nodes in [-1,1] and obtain Pc(x), thecorresponding interpolating polynomial. In the same graph, plot thethree functions f(x), P10(x) and Pc(x) over the interval [-1,1] .Use different line-styles, so that f(x), P10(x) and Pc(x) lookdistinct.
b)Comment on the error formula for the nth degree interpolatingpolynomial by only computing the first three derivatives of f(x).Explain how accuracy will be lost (or gained) by interpolating f(x)at more points (by increasing n)
