%main function call for newton's method
function newton(x0)

%set tol equal to x for convergence purposes
tol=1e5;

%keep track of iterations
count=1;
x = x0;
%do until convergence or too many loops
while tol>1e-10 && count<500

	%newton's method
	%xnew=x-f'(x)/f''(x);
    xnew=x(count)-fprime(x(count))/fdblprime(x(count));
    
    
    x = [x xnew];
	%how close is my iteration
	tol=abs(x(count)-x(count+1));

	%keep track of iteration
	count=count+1;
end
disp(['# of iterations: ',num2str(count)]);
disp(['min/max is: ',num2str(x(end))]);
x1 = linspace(-2,6,100);
y1 = zeros(100,1);
for i=1:100
    y1(i)= f(x1(i));
end
y = zeros(count,1);
for j = 1:count
    y(j) = f(x(j));
end


figure(1);
plot(x1,y1,'-',x,y,'--.')
text(x(1)+.15,y(1)+5,'x0','FontSize',14)
text(x(end)+.15,y(end)+5,'x*','FontSize',14)



function out1 = f(x)

out1 = 10*x^3-50*x^2+2*x+1;


function out2=fprime(x)
    h=eps^(1/3);
    out2=(f(x+h)-f(x))/h;
    
    
    
    
function out3=fdblprime(x)
h = eps^(1/3);
out3 = (fprime(x+h)-fprime(x))/h;