function[f,g,GN]=logistic(b,tvec,yvec)

%  f(X0,M,k,t) = M*X0*exp(kt) / ((M-X0)+X0*exp(kt))  (a)
%              = M*X0 / (X0+(M-X0)exp(-kt))         (b)
%
%  f = .5*r'*r, where r is the residual
%  r = yvec - f(X0,M,k,tvec),
%  g = J'*r,  
%  J = Jacobian of r (use (b) to compute)
%  GN = J'*J 


X0 = b(1);
M = b(2);
k = b(3);

% residual
r = % You fill in here.

%Jacobian
J = % You fill in here.

% f,g,GN
f = .5*r'*r;
g = J'*r;
GN = J'*J;