function [xList, errorList] = NewNewton (f, startingValue, errorAllowed)
%
%NewNewton (f, startingValue, errorAllowed)
%This function computes the root of a function using the modified Newton's method
%

	%Make sure the number of arguments is correct
	if(nargin ~= 3)
		error('That is an incorrect number of arguments')
	end
	%A few necesary things before we get started
	pkg load symbolic;
	warning('off','OctSymPy:sym:rationalapprox');
	%Constant variables
	maxIt = 50;
	fp = diff(f);
	fpp = diff(fp);
	%Variables
	oldAnswer = startingValue;
	newAnswer = 0;
	currentError = errorAllowed + 1;
	cnt = 1;

	%Loop until you find an answer within error or you reach the maximum number of itterations
	while((currentError >= errorAllowed) && (cnt < maxIt))
		newAnswer = oldAnswer - ((double(subs(f,oldAnswer)) * double(subs(fp,oldAnswer)))/(double(subs(fp,oldAnswer))^2 - (double(subs(f,oldAnswer)) * double(subs(fpp,oldAnswer)))));
		currentError = abs(newAnswer - oldAnswer);
		xList(end+1) = newAnswer;
		errorList(end+1) = currentError;
		oldAnswer = newAnswer;
	end
end