function out=NewtonMethod(F,x0,numits,tol)
%  Inputs to Newton's Method:
%     F- Name of a function that returns BOTH 
%        values of g(x) and g'(x)
%     x0= Initial value of x.
%     numits=  Maximum number of iterations
%     tol   =  Tolerance (like 1e-6) measures
%              change between iterates of x
% Example:  We require two outputs, so we need an m-file
%       function [y,dy]=MyFunc(x)
%       y=x^3+x-1;
%       dy=3*x^2+1;
%       end
% Then:  yout=NewtonMethod(@MyFunc,0,100,5e-5);
% Output:  Newton used 5 iterations
%          yout=0.6825

for k=1:numits
   [g,gprime]=F(x0);
   if gprime==0
      error('Derivative is zero');
   end
   xnew=x0-g/gprime;
   d=abs(xnew-x0);
   if d<tol
      out=xnew;
      break
   end
   x0=xnew;
end    
fprintf('Newton used %d iterations\n',k);
out=xnew;