Let X0, 81, ..., Xn be n+1 distinct points with given values f(xo), f(x1)...., f(xn). Let Pn be the Lagrange interpolating polynomial defined using all these points. (a) Give the formulas for the divided differences f[xo), f(x0, X1), and f[:20,21,22). (b) Given Pn(x) f(xo] +a1(x – Xo) + a2(x – Xo)(x – x1) + a3(x – Xo)(x – x1)(x – X2) + +an(x – Xo)(x – x1)... (x – Xn-1), use Pn(x1) to show that aj = f (x0, x1). (c) Given Pn(x) f (xo] + f(x0, x1](x – Xo) + a2(x – xo)(x – Xi) + a3(x – Xo)(x – x1)(x – x2) + ... + an(x – xo)(x – x1)... (x – Xn-1), use Pn(x2) to show that a2 f (x0, X1, X2]