7. Theorem [Interpolation error ) Suppose f(x) is a function that is N times continuously differentiable, and let p(x) be the polynomial of degree N that interpolates f(x) at the points {xi,f(xi)}, i = 0,1,2,...,N. Then for any x (xo,xn) )(0) If(x) P(x) = {'**\wn+1(x)], (N+1)! where c E [X0,XN), and wN+1(x) = (x-xo)(x x1)... (x-Xg). In this problem, we find an upper bound on the error when using quadratic interpolation with equally spaced points, X0, X1, X2. 12 - Xe (a) Let s = x - xy and h = and show that w(x) can be written as 2 w(s) = 53 - h?s, where - hss sh. S, 7. Theorem [Interpolation error ) Suppose f(x) is a function that is N times continuously differentiable, and let p(x) be the polynomial of degree N that interpolates f(x) at the points {xi,f(xi)}, i = 0,1,2,...,N. Then for any x (xo,xn) )(0) If(x) P(x) = {'**\wn+1(x)], (N+1)! where c E [X0,XN), and wN+1(x) = (x-xo)(x x1)... (x-Xg). In this problem, we find an upper bound on the error when using quadratic interpolation with equally spaced points, X0, X1, X2. 12 - Xe (a) Let s = x - xy and h = and show that w(x) can be written as 2 w(s) = 53 - h?s, where - hss sh. S