function xx=bisection1(f,a,b,MaxIterates)
% Basic bisection that returns all the values in the iteration.

y1=f(a); y2=f(b); 

for k=1:MaxIterates
    
   xx(k)=0.5*(a+b);
   y3=f(xx(k));

   %Very special case:
   if y3==0
     fprintf('Whoo hoo!  Root found exactly after %d iterations...\n',k);
     return
   end

   %Reset the interval
   if y1*y3<0
     b=xx(k);
     y2=y3;
   else
     a=xx(k);
     y1=y3;
   end
end
xx(MaxIterates+1)=0.5*(a+b);