Newton's Method 3.166

    public static void main(String[] args) {
        NewtonsMethod(-0.25);
        System.out.println("");
        NewtonsMethod(0.5);
        System.out.println("");
        NewtonsMethod(8.0);
    }

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

        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)-100F*Math.pow(x, 2);
    }

    private static double df(double x) {
        return Math.pow(Math.E, x)-200F*x;
    }