(* MeanValuePlot *)
(* Author: Christopher Moretti *)
(* Version: 1.0 *)
(* MeanValuePlot[fun,{x,a,b}] creates a graphical illustration of the Mean Value Theorem for the function fun on the interval x=a to x=b.  The function is plotted in black, the secant line whose slope is the average rate of change is in red, and the parallel tangent lines are in blue.*)

MeanValuePlot[fun_,xlist_]:=
	Block[{x,a,b,l1,l2,tot,av,i,p,n},
	x=xlist[[1]];a=xlist[[2]];b=xlist[[3]];	
		av=( (fun/. x->b)-(fun/.x->a))/(b-a);
		sols= Select[ (x/. Solve[ D[fun,x]==av,x]), #1>a&&#1<b &];
		l1= Table[ av*(x-sols[[i]])+(fun/. x->sols[[i]]),{i,1,Length[sols]}];
		l2=PrependTo[l1,av*(x-a)+(fun/. x->a)];
		tot=Flatten[{l1,{fun}}];n=Length[tot];
		p[1]=Plot[tot[[1]],{x,a,b},PlotStyle->Hue[2],DisplayFunction->Identity];
		Do[ p[i]=
        Plot[ tot[[i]],{x,a,b},DisplayFunction->Identity,PlotStyle->Hue[.7]],{
        i,2,n-1}];
		p[n]=Plot[fun,{x,a,b},DisplayFunction->Identity];
		Show[Table[p[i],{i,1,Length[tot]}],AspectRatio->Automatic,
      DisplayFunction->$DisplayFunction];
];

MeanValuePlot::usage=
  "MeanValuePlot[fun,{x,a,b}] creates a graphical illustration of the Mean 
Value Theorem for the function fun on the interval x=a to x=b. "

(* Example: MeanValuePlot[x^3-3x,{x,-2,2}] *)