diff --git a/newton_differentiation.m b/newton_differentiation.m
index 2caa7ee..82163e5 100644
--- a/newton_differentiation.m
+++ b/newton_differentiation.m
@@ -13,22 +13,24 @@ function y = b_newt_diff1(Y,h)
 end
 
 
-function y = newt_diff_fr(Y,X,x,h)
+function y = newt_diff_fr1(Y,X,x,h)
 	idx = find(X==x);
 	if (idx == length(X))
-		elems = [X(idx), X(idx-1)]
+		elems = [Y(idx), Y(idx-1)]
 		y = b_newt_diff1(elems,h)
 
 	elseif (idx == 1)
-		elems = [X(idx), X(idx+1)]
+		elems = [Y(idx), Y(idx+1)]
 		y = f_newt_diff1(elems,h)
 	else
-		elems = [X(idx), X(idx+1)]
+		elems = [Y(idx-1), Y(idx+1)]
 		y = c_newt_diff1(elems,h)
 	endif
 	endfunction
 
-
+X = [0 1 2 3 4]
+Y = X.^2
+newt_diff_fr1(Y,X,1,1)
 
 
 
@@ -41,11 +43,11 @@ function y = newt_diff_fr(Y,X,x,h)
 
 
 function y = f_newt_diff2(Y,h)
-	Y =  ( Y(3) - 2 * Y(2) + Y(1) ) / h^2
+	y =  ( Y(3) - 2 * Y(2) + Y(1) ) / h^2
 end
 
 function y = c_newt_diff2(Y,h)
-	Y = ( Y(3) - 2 * Y(2) + Y(1) ) / h^2
+	y = ( Y(3) - (2 * Y(2)) + Y(1) ) / h^2
 end
 
 
@@ -57,18 +59,18 @@ end
 
 
 
-function y = newt_diff_fr(Y,X,x,h)
+function y = newt_diff_fr2(Y,X,x,h)
 	idx = find(X==x);
-	if (idx == length(X))
-		elems = [X(idx), X(idx-1), X(idx-2)]
-		y = b_newt_diff1(elems,h)
+	if (idx == length(X)) %forwards
+		elems = [Y(idx), Y(idx-1), Y(idx-2)]
+		y = b_newt_diff2(elems,h)
 
-	elseif (idx == 1)
-		elems = [X(idx), X(idx+1), X(idx+2)]
-		y = f_newt_diff1(elems,h)
-	else
-		elems = [X(idx-1), X(idx), X(idx+1)]
-		y = c_newt_diff1(elems,h)
+	elseif (idx == 1) %backwards
+		elems = [Y(idx), Y(idx+1), Y(idx+2)]
+		y = f_newt_diff2(elems,h)
+	else % centered
+		elems = [Y(idx-1), Y(idx), Y(idx+1)]
+		y = c_newt_diff2(elems,h)
 	endif
 	endfunction