function xnew=gradient_ex(x0)

% %%%%% Using user-supplied gradient
% options1 = optimset('MaxIter',2,'Disp','off','GradObj','on');
% 
% x1 = -2:0.1:6;
% y1 = zeros(numel(x1),1);
% for i=1:numel(x1)
%   y1(i)=f(x1(i));
% end
% %x0 = 1;
% 
% tol = 1e5;
% x = x0;
% y = f(x0);
% count = 1;
% shift = 20;
% 
% while (tol > 1e-10 && count < 100 )
% [xnew,cost]=fminsearch(@f,x(count),options1);
% 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




% %%%% Not explicitly using the user-supplied gradient
options2 = optimset('MaxIter',2,'Disp','off');

x1 = -2:0.1:6;
y1 = zeros(numel(x1),1);
for i=1:numel(x1)
  y1(i)=f1(x1(i));
end

tol = 1e5;
x = x0;
y = f1(x0);
count = 1;
shift = 0.5;

while (tol > 1e-10 && count < 100 )
[xnew,cost]=fminsearch(@f1,x(count),options2);
x = [x xnew];
ynew = f1(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



%%%%% plotting results  always keep this uncommented! :)
figure(1);
plot(x,y,'--.',x1,y1)
text(x(1),y(1)+shift,'x0','FontSize',14)
text(x(end),y(end)+shift,'x*','FontSize',14)
xlabel('x')
ylabel('y')





function [out1,grad] = f(x)

out1 = 10*x^3-50*x^2+2*x+1;
grad = 30*x^2 - 100*x;




function out2 = f1(x)

out2 = 10*x^3 - 50*x^2+2*x+1;
%out2 = abs(x);