Newton's Method 2.166

    public static void main(String[] args) {
        NewtonsMethod();
    }

    private static void NewtonsMethod() {
        double g = 2.0;
        double tol = Math.pow(10F, -12);

        double old = g+1F;
        int counter = 0;
        while(Math.abs(g-old) > tol) {
            old = g;
            g = old - (f(old)/df(old));
            counter++;
            System.out.println("Iteration " + counter + ": " + g);
        }
    }

    private static double f(double x) {
        return Math.pow(Math.E, x)-3F*x-1;
    }

    private static double df(double x) {
        return Math.pow(Math.E, x)-3F;
    }