It actually does work. The problem is that the red line overplots it since it is plotted later, and hides the blue line. If you make the blue line wider (I set 'LineWidth',3 here) the blue line shows up.
Try this —
% clc; clear all; close all;
fun =@(t) (1/200).*t.^2+(1/500).*exp(-0.2.*t)+5;
dgraph = @(point, dfda, t) dfda*t + (fun(point)-dfda*point);
est_point=150;
da=2;
dfda_true=(1/100).*(150)+(-0.2./500).*exp(-0.2.*(150));
dfda_forward = (fun(est_point+da)-fun(est_point))./da;
dfda_backforward=(fun(est_point)-fun(est_point-da))./da;
dfda_center=(fun(est_point+da)-fun(est_point-da))./(2.*da);
a=-50:0.01:150;
figure(1)
plot(a,fun(a),'k'); hold on;
plot(a, dgraph(est_point,dfda_true,a),'b', 'LineWidth',3); hold on; %dosen't work
plot(a, dgraph(est_point,dfda_center,a),'r'); hold on;
.
