# User talk:Calqtopia

It seems clear that the function $F(x,y,\lambda)$ cannot have a local extremum (at least not a strict one) as at the critical points one has $g(x,y)=c$ so that $F(x*,\,y*,\,\lambda)=F(x*,\,y*,\,\lambda*)$ for all $\lambda$. Though that doesn't quite show it to be a saddle.