1. Implement Newton's method in Matlab to find a root of f(x) = -2 -1 -3 starting with Io = 1.6. Use a tolerance of 1E-8 and report the number of iterations needed. Then implement the Secant Method in Matlab starting with Io = 1.7,11 = 1.67. Use a tolerance of 1E - 8 and report the number of iterations needed. 2a. Modify the Newton's method algorithm to produce the "Accelerated Newton-Raphson Iteration" designed for roots of order M to find a froot of f(x) = (2-1) starting with ro = 1.6 using a tolerance of 1E - 8 and report the number of iterations needed when M = 1,2,5,10. 2b. Do you notice a general trend in the number of iterations vs. the M chosen? 2c. What happens if we take M = 18 or M = 20? Is there a price to pay if we guess the order of the root too large relative to its true order? 3. Redo Problem 6 (above) in Matlab. In Matlab enter matrix as (e.g., A= [1 2:3 4]) where semicolons separate rows. 1. Implement Newton's method in Matlab to find a root of f(x) = -2 -1 -3 starting with Io = 1.6. Use a tolerance of 1E-8 and report the number of iterations needed. Then implement the Secant Method in Matlab starting with Io = 1.7,11 = 1.67. Use a tolerance of 1E - 8 and report the number of iterations needed. 2a. Modify the Newton's method algorithm to produce the "Accelerated Newton-Raphson Iteration" designed for roots of order M to find a froot of f(x) = (2-1) starting with ro = 1.6 using a tolerance of 1E - 8 and report the number of iterations needed when M = 1,2,5,10. 2b. Do you notice a general trend in the number of iterations vs. the M chosen? 2c. What happens if we take M = 18 or M = 20? Is there a price to pay if we guess the order of the root too large relative to its true order? 3. Redo Problem 6 (above) in Matlab. In Matlab enter matrix as (e.g., A= [1 2:3 4]) where semicolons separate rows