function [y,dy,hy]=testfunc(x)
%  A test function for Newton's Method:
%  The input is the VECTOR x (with elements x,y below)
%
%     y = (1/4)x^4-(1/2)x^2+(1/2)y^2
%    dy = Gradient = [x^3-x; y]  (The gradient will output as a COLUMN)
%    hy = Hessian  = [3x^2-1, 0;0,1]

y=(1/4)*x(1)^4-(1/2)*x(1)^(1/2)*x(2)^2;
dy=[x(1)^3-x(1); x(2)];
hy=[3*x(1)^2-1, 0;0,1];