I am solving this exercise:
min $x^2+(y-8)^2$ \begin{cases} y-x^2+2=0 \\ y-7\le0 \end{cases} The solutions are (3,7) and (-3,7) as minima points and (0,-2) as maximum point. For the minima points both constraints are active, hence if I apply the rule for the bordered hessian matrix test which states to look for the (n-m) leading principal minor of the bordered hessian matrix, with n number of variables (x,y)=2 and m number of active contraints (2), I would get n-m=0. So which principal minor should I check in this case?