Question $13(6$ points$)$

Consider the function $f(x,y)=(x-y)(1-xy)$ and the point $P=(1,1).$ Which of the following statements is true?

The second derivative test classifies $P$ as a local maximum of $f$

The second derivative test classifies $P$ as a local minimum of $f$

The second derivative test classifies $P$ as a saddle point of $f$

The second derivative test is inconclusive at $P$

$P$ is not a critical point of $f$ so the second derivative test cannot be applied