4. Recall that a function has a zero Xy of multiplicity m if: f(xs) = 0, f'(:Ls) = 0, ... f(m-1) (s) = 0, f(m) (2 s) 70 (So f is zero at w, and so are its first m - 1 derivatives. But its mth derivative is not.) To find higher multiplicity zeros efficiently we must modify Newton's Method so that: f(3x) 2+1 = 2k - m f'(:22) (m = multiplicity of zero) (a) Make a copy of our Newton's method function newtmeth(x0, f, df, tol), and call it mnewt(m, x0, f, df, tol), where m is the multiplicity of the zero you're looking for. Modify mnewt so that it implements the modified Newton's Method described above. Also modify it so that it prints the number of iterations it used. (b) Let f () = 1 cos(r). Use regular newtmeth and our new program mnewt with m = 2 to find the zero at x = 0. Compare the number of iterations required for cach method by making a table with tolerances of 10-2, 10-4, 10-8. Let xo = 1.0. (e) Let f(x) = 24 23 3.x2 + 5.x 2. Experimentally find the multiplicity of f at x = 1 by using mnewt with different values of m, and comparing the number of iterations required to find the zero. Use Do = 2.0 and a tolerance of 10-8. As usual, make a table. Finally, check that the multiplicity you found experimen- tally is correct by showing: f(m-1)(1) = 0, but f(m) (1) +0. #Perform Newton's Method with starting point xo #on 'f' where 'df' is its derivative until #| x - x1 tol and k tol and k