Consider the function $f(x,y)=x^2+xy-5x-y+1.$ Then:

$(1,3)$ is a critical point and it is a saddle point of $f.$

$(1,3)$ is a critical point and $f$ has a local minimum at $(1,3)$

$(1,1)$ is a critical point and $f$ has a local maximum at $(1,1)$

None of them