Newton's method O solutions submitted (max: Unlimited) Write a MATLAB function, called Newtons_method that inputs a function, f, its derivative f', an initial guess x_0, 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 x_0. Your function should have an error defined by err =|{x_n-x_{n-1}}], 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,xo, tol,N) 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 x_0 = 2, to an accuracy of less than tol = 10^(-8). Did your method converge, and if so, how many iterations did it take? If not, why it did not 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 x_0 = -2. What happens