ClearAll;
f[t_]:= 3t^3 - 14t^2 + 9t + 8;
fPrime[t_]:= 9t^2 - 28t + 9;
(* Find where f'[t] = 0 *)
t1 = t/.Solve[fPrime[t]==0,t][[1]];
t2 = t/.Solve[fPrime[t]==0,t][[2]];
Show[GraphicsArray[{{Plot[f[t],{t,0,4}]},
	{Plot[fPrime[t],{t,0,4},PlotRange->{Automatic,{-13,42}}]}}]];
Print["Global minimum is ",N[f[t2]]]