function x = newton(f, dfdx, x1, maxiter)
% NEWTON   Newton's method for a scalar equation.
%
% Input:
%   f        objective function 
%   dfdx     derivative function
%   x1       initial root approximation
%   maxiter  max number of iterations
%
% Output       
%   x        vector of root approximations (last one is best)

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

    x = x1;  
    y = f(x1);
    dx = Inf;   % for initial pass below
    k = 1;

    while (abs(dx) > xtol) && (abs(y) > funtol) && (k < maxiter)
        dydx = dfdx(x(k));
        dx = -y/dydx;           % Newton step
        x(k+1) = x(k) + dx;
        k = k+1;
        y = f(x(k));
    end

end