Write a Matlab function, called Newtons_method that inputs a function, f, it's derivative f, an initial guess x0, 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 x0. Your function should have an error defined by err =xnxn1, 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,x, tol, N) n is the last iteration when you stop. Use the function you created to find the root of the equation arctanx=1 with initial guess x0=2, to an accuracy of less than tol =108. 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 x0=2. What is happening