function ShowFP_Magnify()
% Show's how roundoff error can be magnified
clc
fprintf('\n\nMaxim 1: Less Can Mean More.\n\n')
x = pi/3;
disp('If x = pi/3, then sin''(x) = cos(x) = 1/2.')
disp('Using divided differences:')
disp(' ')
disp(' h (sin(x+h)-sin(x))/h error')
disp('-------------------------------------------')
for h=logspace(-1,-15,15)
divdiff = (sin(x+h)-sin(x))/h;
fprintf('%10.2e %18.15f %10.2e\n',h,divdiff,abs(divdiff-1/2))
end