EXTRA PROBLEM (4 pts.): Let Pn interpolate f at n+1 distinct points. Consider Pn in its Lagrange and Newton forms n n n j-1 Pn(x) = a; II (2 ) = c; II(2 Xx) j=0 k=0,k#j j=0 k=0 with a; = = f(x;) TIX=0,k+i 1/(x; xk) and c; = f[10,...,x]. Suppose that we will evaluate Pn many times for different values of x. Thus, we can precompute the values of a; and c; and then can use them without any cost. For both forms, propose efficient (in terms of arithmetic operations) algorithms for computing Pn(x). Which form admits less expensive algorithm? 1