For the following question, your submission should contain 3 Matlab functions and a Matlab script.

(a) Create a Matlab program function that applies Newtons method for a given function f, its derivative f1, an initial guess x0, and a predetermined tolerance for residue tol. This program should output x: the estimate for the root of f with residue smaller then tol, n: the number of iterations the program used to reach the specified tolerance.

(b) Create a Matlab program function that applies false position method for a given function f, initial guesses x0 and x1, and a predetermined tolerance for residue tol. This program should output x: the estimate for the root of f with residue smaller then tol, n: the number of iterations the program used to reach the specified tolerance.

(c) Create a Matlab program function that applies the bisection method for a given function f, initial guesses a and b, and a predetermined tolerance for residue tol. This program should output x: the estimate for the root of f with residue smaller then tol, n: the number of iterations the program used to reach the specified tolerance.

(d) Create a Matlab script function that uses the functions created in (a), (b) and (c) for the function f = x 27 10 with tolerances 0.1, 0.01, 0.001, 0.0001, 0.00001, 0.000001, 0.0000001, 0.00000001, 0.000000001, 0.0000000001. Also take x0=1 for (a), x0=5,x1=15 for (b) and a=0, b=15 for (c).

(e) Report and compare the results of these calculations as comments on your script file