ClearAll;Clear[f1];Clear[f2];
$DefaultFont = {"Times-Roman",10};
Needs["Statistics`DataManipulation`"];
Needs["Graphics`Graphics`"];
cumulative = {312/545,413/545,487/545,522/545,537/545,1};
datapoints = {{0,0},{1,312/545},{2,413/545},
			  {3,487/545},{4,522/545},{5,537/545},{6,1}};
density = {312/545,101/545,74/545,35/545,15/545,8/545};
F1[A_,c_,x_] = 4 A c x/(1 + A c^2) - A x^2;
F2[A_,c_,x_] = 1 - ((1 - A c^2)^2 (c/x)^(2A c^2/(1 - A c^2)))/(1 + A c^2);

f1[A_,c_,x_] = 2 A(c-x) + 2 A c(1 - A c^2)/(1 + A c^2);
f2[A_,c_,x_] = (2A c(1 - A c^2) (c/x)^((1 + A c^2)/(1 - A c^2)))/(1 + A c^2);

FF[a_,c_,x_] = Which[x<=1.5,F1[a,c,x],x>1.5,F2[a,c,x]];

error[a_,c_] = Evaluate[Apply[Plus,Table[(FF[a,c,n]-cumulative[[n]])^2,{n,1,6}]]];
leasterror = FindMinimum[error[a,c],{a,0.1,0.2,0,0.4},{c,2,2.2,1,2}]

aopt = a/.leasterror[[2]]; copt = c/.leasterror[[2]];
				
dot = leasterror[[1]] + 0.00000005;
Show[ContourPlot[error[a,c],{a,0.12,0.15},{c,1.7,2},
			ContourShading->False,
			Contours->{0.006575,0.0066,0.00665,0.0067,0.00675,0.0068,0.0118,0.0168,0.0218,0.0268},
			Frame->False,
			PlotPoints->150,
			Axes->True,
			AspectRatio->1/GoldenRatio,
			PlotLabel->"     Figure 24.4\n\n S(A,c) = constant",
			AxesLabel->{"A","c"}]]