hold off

x=[pi/6:0.01:pi];
v=1./x.*sin(x)-cos(x).*1./(x+1);
plot(x,v,'LineWidth',3);

hold on
plot(x(1),v(1),'b.', 'MarkerSize',30);
plot(x(1),0,'k.','MarkerSize',30);                  
text(x(1),-0.1,'a','FontSize',20)
                   plot(x(end),v(end),'.','MarkerFaceColor','b',...
                       'MarkerSize',30);
plot(x(end),0,'k.','MarkerSize',30);                   
text(x(end),-0.1,'b','FontSize',20)
                   M(2) = getframe;

yy=[-0.1:0.01:1];
plot(zeros(size(yy)),yy,'k','LineWidth',2)
xx=[-0.1:0.01:pi+0.1];
plot(xx,zeros(size(xx)),'k','LineWidth',2)
grid minor
pause

m=(v(end)-v(1))/(x(end)-x(1));
q=v(1)-m*x(1);
plot(x,m*x+q,'r','LineWidth',3);
qq=[q 0.62 0.70  0.730];
pause

for j=2:size(qq,2)
  
 plot(x,m*x+qq(j),'r-','LineWidth',2)

 pause
 

end  
plot(x,m*x+qq(end),'r','LineWidth',3)

hold off
plot(x,v,'LineWidth',3);

hold on

plot(x(1),v(1),'b.','MarkerSize',30);
plot(x(1),0,'k.','MarkerSize',30);                  
text(x(1),-0.1,'a','FontSize',20)
plot(x(end),v(end),'b.','MarkerSize',30);
plot(x(end),0,'k.','MarkerSize',30);                   
text(x(end),-0.1,'b','FontSize',20)


plot(zeros(size(yy)),yy,'k','LineWidth',2)
xx=[-0.1:0.01:pi+0.1];
plot(xx,zeros(size(xx)),'k','LineWidth',2)
grid minor
                   
plot(x,m*x+q,'r','LineWidth',3);
plot(x,m*x+qq(end),'r','LineWidth',3)

pause

x1=1.6+0.075;plot(x1*ones(size([0:0.01:1./x1.*sin(x1)-cos(x1).*1./(x1+1)])),[0:0.01:1./x1.*sin(x1)-cos(x1).*1./(x1+1)],'k -','LineWidth',2)
text(1.65,-0.1,'c','FontSize',20)
plot(x1,0,'k.','MarkerSize',30);