Auxiliary Definitions (do not display)

>	f8 := (x^3-3*x^2-x)/(x^2-4): P1 := FunctionChart( f8, -10..16, view=[DEFAULT,-20..20],                      pointoptions=[symbolsize=20],                      slope=[thickness(2,2), color(red,blue)],                      concavity=[filled(pink,cyan)] ):

>	S1 := SignChart( f2, x=-10..10, [0,1,2] ): P1 := display( S1, title=sprintf("Sign Chart for\n y=%a",f2) ):

>	f2 := (-x^3+3*x^2-5*x+6)/(x^2-4*x+3): P2 := FunctionChart( f2, -10..15, view=[DEFAULT,-20..10],                      pointoptions=[symbolsize=20],                      slope=[thickness(2,2), color(red,blue)],                      concavity=[filled(pink,cyan)] ):

>

f3 := sin(x)^2: a3 := 0: b3 := 3*Pi/2: msec3 := (eval(f3,x=b3)-eval(f3,x=a3))/(b3-a3): P3 := plot( [f3, seq(msec3*x+c/8,c=-8..8)], x=a3..b3, color=[red,blue$8,green,blue$8],             discont=true,             title="Visual Proof that MVT does apply to\nf(x)=sin(x)^2 on [0,3*Pi/2]" ): P4 := MeanValueTheorem( f3, a3..b3, output=plot, view=[DEFAULT,-1..2] ):

>	#P1; P2; P3; P4;