3. Write a MATLAB function, called Newtons_method that inputs a function, f, it's derivative f', an initial guess o, an error tolerance, tol, and a maximum number of iterations, N, and outputs the root of f obtained using Newton's method (denoted by c), starting with xo. Your function should have an error defined by err= |Zn-Zn-11, and stop when the error is less than the tolerance, or if the number of iterations exceeds N - whichever happens first. Your function header should look something like: function [c, n, err] Newtons-method (f, fp, x0,tol,N) = where n is the last iteration when you stop. Use the function you created to find the root of the equation arctan(x)-1 with initial guess xo-2, to an accuracy of less than e 10-8. Did your method converge, and if so, how many iterations did it take? If not, why didn't it converge, and what happened-did it diverge, or end up in an infinite loop? Plot on the same graph the function and the axis y = 0. Test with 20 =-2. What is happening