Consider approximating 1/3 on a computer using Newton's method to solve f(x) = 3 - 1 = 0. 1) Derive the formula for Newton's method for this problem. 2) Modify newton.m (or write your own program) and write another script to call newton.m to compute 1/3 with e = 10-5 and max iter = 30 and tabulate the results as in Table 3.2 on page 81. Try three different initial guesses: 20 0.1,0.2, 0.3 and describe your observations in connection with the theory