function x = newton(f,fprime,x0)
% NEWTON   Newton's method for a scalar equation.
% Input:
%   f        function that outputs values of f(x)
%   fprime   function that outputs values of f'(x)
%   x0       initial root approximation
% Output       
%   x        vector of root approximations (last is best)

% Operating parameters.
funtol = 100*eps;  xtol = 100*eps;  maxiter = 40;

x = x0;  fn = f(x0);
dx = Inf;  
n = 1;

while (abs(dx) > xtol) & (abs(fn) > funtol)
  dfn = fprime(x(n));
  dx = -fn/dfn;   % Newton step
  x(n+1) = x(n) + dx;

  n = n+1;
  if n==maxiter
    warning('Maximum number of iterations reached.')
    break
  end

  fn = f(x(n));
end