ClearAll;
$DefaultFont = {"Times-Roman",10};
Needs["Graphics`Graphics`"];
ylow = -0.4; yhigh = 8;
G[t_]:= 1/(2.1-t) - t^2;
GP[t_]:= D[G[x],x]/.x->t;
xcross[z_]:= z - G[z]/GP[z]; 
xhigh[z_,c_]:= (c - G[z])/GP[z] + z;
chord[z_,c_]:= Graphics[{Dashing[{0.001,0.01}],
				  Line[{{xcross[z],0},{xhigh[z,c],c}}]}];
vert[z_]:= Graphics[{Thickness[0.001],Line[{{z,0},{z,G[z]}}]}];
tstar = t/.FindRoot[G[t]==0,{t,2}];
				  
circ[u_,v_]:= Graphics[Disk[{u,v},{0.0027,0.09}],
	AspectRatio->Automatic];
plot = Plot[G[t],{t,1,2.05},PlotPoints->500,
			PlotLabel -> "Figure 16.4\n\n  y = G(t)",
			AxesOrigin->{1.68,0},AxesLabel->{"t","y"},
			Ticks->{{{1.99,Subscripted[t[0]]},
			{xcross[1.99],Subscripted[t[1]]},
			{xcross[xcross[1.99]],Subscripted[t[2]]},{tstar,"t*"}},
			{{0.001,"0"},
			{G[1.99],Subscripted[y[0]]},
			{G[xcross[1.99]],Subscripted[y[1]]},
			{G[xcross[xcross[1.99]]],Subscripted[y[2]]}}},
			PlotRange->{{1.7,2.065},{ylow,yhigh}}];
Show[plot, vert[1.99],circ[1.99,G[1.99]],chord[1.99,yhigh],
		   vert[xcross[1.99]],chord[xcross[1.99],3],
		   circ[xcross[1.99],G[xcross[1.99]]],
		   vert[xcross[xcross[1.99]]],
		   chord[xcross[xcross[1.99]],1],
		   circ[xcross[xcross[1.99]],G[xcross[xcross[1.99]]]],
		   Graphics[Text["A",{1.985,G[1.99]}]],
		   Graphics[Text["B",{xcross[1.99],G[xcross[1.99]]+0.2}]],
		   Graphics[Text["C",{xcross[xcross[1.99]],G[xcross[xcross[1.99]]]+0.2}]]]