6. (10 points) Consider the data set D3 = {(0, 1), (2, ), (4, ;) }. (a) Construct the divided-difference table associated with D3, and then write down the associated degree-2 Newton interpolating polynomial p2(x). (b) Suppose P(x) is the (degree n - 1 or less) polynomial which interpolates the smooth function f(x) at the points X1, . .., In, that is P(Ck) = f(Xk) for k = 1, ..., n. Write down an exact formula for the interpolation error f(x) - P(x). Define any notation you introduce. (c) Using the formula from (b), estimate the error If(1)-p2(1) | in using p2(1) to approximate f(1), where f(x) = 1/(x + 4) gives the data D3 from (a). Compare with the exact error