close all; clear all; clc;
h = figure;
axis tight manual % this ensures that getframe() returns a consistent size
filename = 'DiffQuot.gif';

x=[-1:0.01:3];
y = inline('-(2/5 - (exp(-t).*(2*cos(2*t) + sin(2*t)))/5)','t');
%y=2/5 - (exp(-x).*(2*cos(2*x) + sin(2*x)))/5; 
a=-0.5; 

for b=3:-15*0.005+0.000000001*randn:a
    plot(x,y(x),'LineWidth',2); hold on;
    plot(a, y(a),'k.','MarkerSize',18);
    plot(b, y(b),'k.','MarkerSize',18);
    m=(y(b)-y(a))/(b-a);
    yy=m*(x-a)+y(a);
    plot(x,yy,'LineWidth',1.5); axis([-1 3 min(y(x))-0.1 max(y(x))+0.1]);
    plot([a a],[-1.2 0],'k'); plot([b b],[-1.2 0],'k');
    plot([a b],[-1 -1],'k'); plot([a b],[y(a) y(a)],'g--','LineWidth',1.5); plot([b b],[y(a) y(b)],'r--','LineWidth',1.5); 
    if abs(b-a)>0.01
        text((b+a)/2,-1.1,['$h\approx$',num2str(b-a)],'fontsize',20,'interpreter','latex');
        text(-0.5,-1.34,['$\frac{\emph{rise}}{\emph{run}}=\frac{f(x+h)-f(x)}{h}\approx\,\, $',num2str(y(b)-y(a),3),'/',num2str(b-a,3)],'fontsize',20,'interpreter','latex');
        text(2.2,-1.34,['$\approx\,\, $',num2str(m,3)],'fontsize',20,'interpreter','latex');
    else
        text((b+a)/2,-1.1,'$h=0$','fontsize',20,'interpreter','latex');
        text(-0.5,-1.34,['$\frac{\emph{rise}}{\emph{run}}=\frac{f(x+h)-f(x)}{h}\approx\,\, $',num2str(m,3)],'fontsize',20,'interpreter','latex');
    end
    xlabel('$x$','fontsize',20,'interpreter','latex'); ylabel('$y$','fontsize',20,'interpreter','latex');
    drawnow; hold off;
    % Capture the plot as an image 
      frame = getframe(h); 
      im = frame2im(frame); 
      [imind,cm] = rgb2ind(im,256); 
      % Write to the GIF File 
      if b == 3 
          imwrite(imind,cm,filename,'gif', 'Loopcount',inf); 
      else 
          imwrite(imind,cm,filename,'gif','WriteMode','append'); 
      end
end