I'm trying to analyze the critical behavior of the function $f(x,y)=x^2-2xy+y^2$ at the origin $(0,0)$. Specifically, is the critical point non degenerate? Isolated? A local max or min?
Since the Hessian matrix is singular, we can't use this to conclude anything about the local extrema. However, graphing this function makes it clear that there is an absolute minimum at $0$.
How can I go about showing this without just saying "look at the graph"?