function xnew=direct_ex(x0)

options = optimset('MaxIter',2,'Disp','off');
%x0 = 1;
tol = 1e5;
x = x0;
y = f(x0);
count = 1;
while (tol > 1e-10 && count < 100 )
[xnew,cost]=fminsearch(@f,x(count),options);
x = [x xnew];
ynew = f(xnew);
y = [y ynew];
disp(['The new point is: ',num2str(xnew)])
disp(['The residual is: ',num2str(cost)])
count = count+1;
tol = abs(x(count) - x(count-1));
end


x1 = -2:0.1:6;
y1 = zeros(numel(x1),1);
for i=1:numel(x1)
    y1(i)=f(x1(i));
end

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



function out1 = f(x)

out1 = 10*x^3-50*x^2+2*x+1;
%out1 = abs(x);