% FOURTH ORDER
% 
% Function : Y = a x^4 + b x^2
X = [0.5,1.5];
X = X';


A = [X.^4,X.^2];

% Y = A * [a;b]
Ai = inv(A);

dxc = [4*X.^3,2*X];
% dy/dx = dxc * [a;b]

d2xc = [12*X.^2,2*ones(size(X))];
% d2y/dx2 = d2xc * [a;b]

disp('18*d/dx:')
disp(18*dxc*Ai)

disp('18*d2/dx2:')
disp(18*d2xc*Ai)

return
% Third ORDER
X = 0:3;
X = X';

A = [X.^3,X.^2,X,ones(size(X))];
Ai = inv(A);

dxc = [3*X.^2,2*X,ones(size(X)),zeros(size(X))];
d2xc = [6*X,2*ones(size(X)),zeros(size(X)),zeros(size(X))];

disp('6*d/dx:')
disp(6*dxc*Ai)

disp('6*d2/dx2:')
disp(6*d2xc*Ai)

return