Section 3.4 Examples
Calculus I
Andy Long

Clear["Global`*"]

(* #7, p. 234 *)
f[x_]:=(3x^2-x+4)/(2x^2+5x-8)
a[x_]:=3/2
Plot[{f[x],a[x]},{x,0,50}]

(* #8, p. 234 *)
f[x_]:=Sqrt[(12x^3-5x+2)/(1+4x^2+3x^3)]
a[x_]:=2
Plot[{f[x],a[x]},{x,0,50}]

(* #16, p. 234 *)
f[x_]:=x^2/Sqrt[(x^4+1)]
a[x_]:=1
Plot[{f[x],a[x]},{x,0,50}]

(* #26, p. 234 *)
f[x_]:=(1+x^6)/(x^4+1)
a[x_]:=x^2
Plot[{f[x],a[x]},{x,0,4}]

(* #24, p. 234 *)
f[x_]:=Sqrt[x^2+1]
a[x_]:=Abs[x]
Plot[{f[x],a[x]},{x,-10,10}]

(* #44, p. 235 *)
f[x_]:=(1+2x^2)/(1+x^2);
f[x]
Plot[{f[x],f'[x],f''[x],2},{x,-3,3},PlotRange->{-1,3}]

(* #49, p. 236 *)
f[x_]:=x^4-x^6;
f[x]
Plot[{f[x],f'[x],f''[x]},{x,-2,2},PlotRange->{-1.5,1.5}]

(* #50, p. 236 *)
f[x_]:=x^3(x+2)^2(x-1);
Plot[{f[x]},{x,-3,2},PlotRange->All]
Plot[{f[x],-4x^3},{x,-2,1}]

(* Example 4, p. 228 *)
f[x_]:=Sqrt[2x^2+1]/(3x-5);
f[x]
Plot[f[x],{x,-2,4},PlotRange->{-3,3}]
Plot[{f[x],f'[x],f''[x],Sqrt[2]/3,-Sqrt[2]/3},{x,-2,4},PlotRange->{-1,1}]