function [retval] = q2 (input1, input2)
format long
f = @(x) cos(x);
w = ones(4,5);
w(1:4,1:2) = [.6 f(.6) ; .7 f(.7) ; .8 f(.8) ; .9 f(.9) ];
for i = 1:3
  w(i,3) = (w(i+1,2) - w(i,2))/(w(i+1,1) - w(i,1));
end
for i = 1:2
  w(i,4) = (w(i+1,3) - w(i,3))/(w(i+2,1) - w(i,1));
end
for i = 1:1
  w(i,5) = (w(i+1,3) - w(i,3))/(w(i+3,1) - w(i,1));
end
%%  You may see the w.
 disp(w);


g = @(x) w(1,5)*(x-w(1,1))*(x-w(2,1))*(x-w(3,1)) + w(1,4)*(x-w(1,1))*(x-w(2,1)) + w(1,3)*(x-w(1,1)) + w(1,2) - x;
%%  That is, g(x)=cos(x)-x by interpolaion of the four points.
%%  Therefore, I'd like to find the root of g(x).

a = -10;
b = 10;
ga = g(a);
gb = g(b);
c = (a+b)/2;
gc = g(c);

for i = 1:5000

  if gc*ga < 0
    gb = gc;
    b = c;
  elseif gc*gb < 0
    ga = gc;
    a = c;
  end
  
  c = (a+b)/2;
  gc = g(c);
  if abs(gc) < 10^-30
    fprintf('   After %d times, \n', i+1 );
    fprintf('   when x = %.30f,\n     g(x) = %.30f.\n', c , g(c) );
    break
  end
  
end

endfunction