Please show matlab code. Will upvote.

3. Do Exercise 3.9 in NCM. The task for you in part (b) is to play with the distribution of the data points (by modifying line 64 of rungeinterp.m or adding alternatives) and find a distribution that works much better than the default equal spacing. There is also a rigorous mathematical proof supporting this part of the problem (and the more mathematically/theoretically inclined among you may want to look it up). 9. The M-file rungeinterp.m provides an experiment with a famous polynomial interpolation problem due to Carl Runge. Let f(x)=1+25x21, and let Pn(x) denote the polynomial of degree n1 that interpolates f(x) at n equally spaced points on the interval 1x1. Runge asked whether, as n increases, Pn(x) converges to f(x). The answer is yes for some x, but no for others. (a) For what x does Pn(x)f(x) as n ? (b) Change the distribution of the interpolation points so that they are not equally spaced. How does this affect convergence? Can you find a distribution so that Pn(x)f(x) for all x in the interval