function [Nx,iter]=newton1(xinit,maxiters)
%FUNCTION Nx=newton1(xinit,maxiters)
%
%This is a sample function to perform Newton's Method.
%The functions are defined within this program.
%  Input:  xinit = initial guess
%          maxiters=  maximum times to iterate
%  Output:  Nx = approximate solution
%           iter= the iteration at which we stopped.
%
%  Sample useage:  [x,iter]=newton1(0.6,500);
%
% This is a sample program; if we were doing this
%   for real we'd want better stopping criteria and
%   a different method of calling F and dF.

xinit=0.3;

x=xinit;
for i=1:maxiters  %100 is the max number of iterations we'll try
    y=F(x);
    dy=dF(x);
    if abs(dy)>0.00001
       Nx=x-(F(x)/dF(x));
       x=Nx;
    else
       iter=i;
       break
    end
 end
 iter=maxiters;
 
 
 function y=F(x)
 y=cos(x)-x;
 return
 
 function dy=dF(x)
 dy=-sin(x)-1;
 return