ClearAll;
R[t_]:= Which[t<2,t(3-t)/4,t>=2,1/t];
RPrime[t_]:= Which[t<2,3/4 - t/2,t>=2,-t^(-2)];
plotR = Plot[R[t],{t,0,9.6},PlotRange->{{0,10},{0,0.6}},
				  AxesLabel->{"y","t"},
				  Ticks->{Table[2k,{k,1,5}],Table[0.1k,{k,0,5}]},
			      PlotLabel->FontForm["y = R(t)",{"Courier",10}]];
plotRPrime = Plot[RPrime[t],{t,0,9.6},PlotRange->{{0,10},{-0.255,0.8}},
				  AxesLabel->{"y","t"},Ticks->{{1,3,10},{-0.2,0,0.2,0.4,0.6}},
			      PlotLabel->FontForm["y = R'(t)",{"Courier",10}]];
Show[GraphicsArray[{{plotR},{plotRPrime}}]]