Cleaned up the file

To use:
Set startPt to an x sub 1 of your choosing.
Choose the amount of approximations that you would like to try.
Put the function and derivative into the file, and it will work.

Currently using the function f(x) = cos(x) - x

newtonRaphson.java

@@ -1,6 +1,5 @@
 /**
- * A program using the Newton-Raphson method to get a solution to its 
- * sixth decimal.
+ * A program using the Newton-Raphson method to approximate a solution.
  * 
  * @author William Carr
  * @version 11.21.2022
@@ -14,93 +13,48 @@ public class newtonRaphson {
 	 */
 	public static void main(String[] args) {
 
-//		//starting point
-//		double ans = 1;
-//		System.out.println(ans);
-//		
-//		//points that newton-raphson method leads to
-//		for(int i = 0; i < 7; i++) {
-//			ans = newtonRaphsonMethod(ans, oneA(ans), oneAPrime(ans));
-//			System.out.println(ans);
-//		}
-
-		double startPt = 2;
-		int approximations = 3;
+		double startPt = 1; //x sub 1 for our purposes
+		int approximations = 10; //how many approximations do we attempt?
 
+		System.out.println("x sub 1:\t" + startPt);
 		thirdNewtonRaphsonMethod(startPt, approximations);
 
-		// TLDR: all the methods work exactly the same and I should have started on github
-//		double first = firstNewtonRaphsonMethod(startPt, function(startPt), derivative(startPt), approximations);
-//		double second = secondNewtonRaphsonMethod(startPt,  approximations);
-//		double third = thirdNewtonRaphsonMethod(startPt, approximations);
-//		System.out.println(first == second);
-//		System.out.println(second == third);
-
 	}
 
 	/**
-	 * Uses the Newton-Raphson method to find an estimated value. 
-	 * Side Note: I tried making it recursive first before realizing it would be easier to read a simple for loop version.
-	 * Question: Is it bad to use xN in the loop? I notice that normally in code that I have seen,
-	 * programmers avoid modifying the parameters like that.
+	 * Uses the Newton-Raphson method to find an estimated value.
 	 * 
 	 * @param xN The x sub 1 to be used for this equation.
 	 * @param approximation The highest level of approximation to attempt. Must be >= 1.
 	 * @return The base value after doing the method a certain number(<iterations>) of times
 	 */
-	public static double thirdNewtonRaphsonMethod(double xN, int approximation) { //most shortened version, but I'm not sure if this is something that CS people avoid on purpose
-		for(int i = 0; i < approximation; i++) {
+	public static double thirdNewtonRaphsonMethod(double xN, int approximation) {
+		for(int i = 1; i < approximation; i++) { // xN is x sub 1, so we skip the first index
 			xN = xN - function(xN)/derivative(xN);
-			System.out.println(xN);
+			System.out.println("x sub " + (i+1) + ":\t" + xN);
 		}
 
 		return xN;
 	}
 
-//	public static double secondNewtonRaphsonMethod(double xN, int approximation) {
-//		//takes the first iteration of the method
-//		double x = xN - function(xN)/derivative(xN);
-//		System.out.println(x);
-//		
-//		for(int i = 1; i < approximation; i++) { // starts at i = 1; because the first approximation was already completed
-//			x = x - function(x)/derivative(x);
-//			System.out.println(x);
-//		}
-//		
-//		return x;
-//	}
-//	
-//	public static double firstNewtonRaphsonMethod(double xN, double f, double fPrime, int iterations) {
-//		double x = xN - f/fPrime;
-//		System.out.println(x); //comment this line if you do not want to see every x sub n in the whole process
-//		
-//		//recursion stops when we have reached the last iteration that we are attempting for
-//		if(iterations == 1) {
-//			return x;
-//		}
-//		//runs the next iteration
-//		return firstNewtonRaphsonMethod(x, function(x), derivative(x), iterations-1);
-//	}
-
-
 	/**
-	 * Formula for original function
+	 * Formula for original function. Must exist at x.
 	 * 
-	 * @param x Any x in the domain of f(x)
+	 * @param x Any x in the domain of f(x).
 	 * @return f(x)
 	 */
 	public static double function(double x) {
-		return Math.pow(x, 3) - 2 * x - 5;
+		return Math.cos(x) - x;
 	}
 
 	/**
-	 * Formula for the derivative of the function
+	 * Formula for the derivative of the function. Must be differentiable at x.
 	 * 
-	 * @param x Any x in the domain of f(x)
+	 * @param x Any x in the domain of f(x) and f'(x).
 	 * @return f'(x)
 	 */
 	public static double derivative(double x) {
-		return 3 * Math.pow(x, 2) - 2;
+		return -1 * Math.sin(x) - 1;
 	}
 
 }