%Finite Centered Difference: This m-file will compute the derivative of a
%hardwired function (x^5)

h=10.^(-20:1);                                      %given h-values

deriv_approx=[(1+h).^5-(1-h).^5]./(2.*h);           %finite centered derivative for each value of h
difference=deriv_approx-5;                          %difference between finite centered difference and true value

figure;                                                 %set up new plotting area
subplot(2,1,1);semilogx(h,deriv_approx,'o');            %set up sub-plot and draw semilog plot 
axis([0 h(20) 0 10]);
xlabel('h value'); ylabel('derivate of x^5 at x=1');

subplot(2,1,2);semilogx(h,difference,'x');
axis([0 h(20) 0 1]);
xlabel('h value'); ylabel('difference between der and true value');