(* p. 137, #48, 58, 64: *)

(* p. 137, #48: Notice the symmetry. f is odd, so its derivative is even. *)
f[x_]:=x+1/x;
Plot[f[x],{x,-2,2},PlotRange->{-10,10}]
Plot[{f[x],f'[x]},{x,-2,2}]

(* p. 137, #58: *)
f[x_]:=Sqrt[x]/(x+1);
Together[f'[x]]
(* Observe how I put the tangent line into the plot: in point-slope form: *)
Plot[{f[x],f'[4](x-4)+f[4]},{x,0,6}]
Plot[{f[x],f'[x]},{x,0,6}]

(* p. 137, #64: *)
s[t_]:=t^4-2t^3+t^2-t;
s'[t]
s''[t]
s''[1]
Plot[{s[t],s'[t],s''[t]},{t,0,6}]
{s[6],s'[6],s''[6]}