Measuring the Degree of Differentiability of Function

I believe the idea was that functions with a greater rate of change are "less" accurately differentiable, in a sense.

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import java.util.Scanner;

public class degreeOfDifferentiability {

	/**
	 * e^x, as array, differentiate at two points using the same h, then compare
	 * with instantaneous rate of change with smaller h.
	 */

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner scan = new Scanner(System.in);
		double x1;
		double x2;
		double h1 = .0001;
		double h2 = .00001;
		double instantaneousy1h1;
		double instantaneousy2h1;
		double instantaneousy1h2;
		double instantaneousy2h2;

		grapher function = new grapher();
		String point;

		System.out
				.println("Do you want to compare the differentiability of the entire function 2^x or at a point? Respond 'function' or 'point'");
		point = scan.next();

		if (point == "point") {
			System.out
					.println("The equation is 2^x, at what points do you want to compare the degree of differentiability?");
			x1 = scan.nextDouble();
			x2 = scan.nextDouble();

			instantaneousy1h1 = ((function.evaluateAtPoint(2, x1 + h1) - function
					.evaluateAtPoint(2, x1))
					/ h1
					+ function.evaluateAtPoint(2, x1) - function
					.evaluateAtPoint(2, x1 - h1)) / 2;
			instantaneousy2h1 = ((function.evaluateAtPoint(2, x2 + h1) - function
					.evaluateAtPoint(2, x2))
					/ h1
					+ function.evaluateAtPoint(2, x2) - function
					.evaluateAtPoint(2, x2 - h1)) / 2;
			instantaneousy1h2 = ((function.evaluateAtPoint(2, x1 + h2) - function
					.evaluateAtPoint(2, x1))
					/ h2
					+ function.evaluateAtPoint(2, x1) - function
					.evaluateAtPoint(2, x1 - h2)) / 2;
			instantaneousy2h2 = ((function.evaluateAtPoint(2, x2 + h2) - function
					.evaluateAtPoint(2, x2))
					/ h2
					+ function.evaluateAtPoint(2, x2) - function
					.evaluateAtPoint(2, x2 - h2)) / 2;
			System.out.println(instantaneousy1h1 + "," + instantaneousy2h1
					+ "," + instantaneousy1h2 + "," + instantaneousy2h2);
			System.out.println(instantaneousy1h1 - instantaneousy1h2);
			System.out.println(instantaneousy2h1 - instantaneousy2h2);
		}

		if (point == "function") {

			for (double i = 0; i < 10; i += .01) {
				instantaneousy1h1 = ((function.evaluateAtPoint(2, i + h1) - function
						.evaluateAtPoint(2, i))
						/ h1
						+ function.evaluateAtPoint(2, i) - function
						.evaluateAtPoint(2, i - h1)) / 2;
				instantaneousy2h1 = ((function.evaluateAtPoint(2, i + h1) - function
						.evaluateAtPoint(2, i))
						/ h1
						+ function.evaluateAtPoint(2, i) - function
						.evaluateAtPoint(2, i - h1)) / 2;
				instantaneousy1h2 = ((function.evaluateAtPoint(2, i + h2) - function
						.evaluateAtPoint(2, i))
						/ h2
						+ function.evaluateAtPoint(2, i) - function
						.evaluateAtPoint(2, i - h2)) / 2;
				instantaneousy2h2 = ((function.evaluateAtPoint(2, i + h2) - function
						.evaluateAtPoint(2, i))
						/ h2
						+ function.evaluateAtPoint(2, i) - function
						.evaluateAtPoint(2, i - h2)) / 2;
				System.out.println(instantaneousy1h1 - instantaneousy1h2);
				System.out.println(instantaneousy2h1 - instantaneousy2h2);
			}

		}

	}

}