function [xList,errorList] = Newton (f, startingValue, errorAllow)
%
%This function uses Newtons method to find a solution to the root of f
%

	pkg load symbolic;
	warning('off','OctSymPy:sym:rationalapprox');
	maxIt = 50;
	fp = diff(f);
	oldAnswer = startingValue;
	newAnswer = 0;
	cnt = 1;
	currentError = errorAllow + 1;

	%Loop until the error becomes small enough or the maximum number of itterations is met
	while((cnt < maxIt) && (currentError > errorAllow))
		newAnswer = oldAnswer - (double(subs(f,oldAnswer))/double(subs(fp,oldAnswer)));
		currentError = abs(newAnswer - oldAnswer);
		xList(end+1) = newAnswer;
		errorList(end+1) = currentError;
		oldAnswer = newAnswer;
		++cnt;
	end
end