%Finite Centered Difference min: This m-file will compute the compare the
%maximum accuracy obtainable with the finite centered difference to the
%maximum accuracy obtainable with the finite forward difference for there
%respective values of hmin

h=10.^(-20:.01:1);                                      %given h-values

fc_deriv_approx=[(1+h).^5-(1-h).^5]./(2.*h);            %finite centered derivative for each value of h
ff_deriv_approx=[(1+h).^5-(1).^5]./h;                   %finite forward derivative for each value of h    

fc_difference=fc_deriv_approx-5;                        %difference between finite centered difference and true value
ff_difference=ff_deriv_approx-5;                        %difference between finite forward difference and true value

abs_fc_difference=abs(fc_difference);                   %need absolute value or else we'll get -5 for h=0.
abs_ff_difference=abs(ff_difference);

[C1,I1]=min(abs_fc_difference)                          %find minimum error/maximum accuracy for each case 
[C2,I2]=min(abs_ff_difference)                          %and index at which it occurs for each

h(I1)  

h(I2) 