Since

the function has only one critical point, namely, . But it is neither a point of local maximum, nor a point of local minimum. For example for every ,

and

Thus, is in fact a saddle point for .

It is easy to check that is a critical point for . Along the line , which passes through ,

and hence takes both positive and negative values at points as close to as we want. Since , the point is a saddle point for .