Chapter 14.7, Problem 2PT

To determine

The appropriate option for the statement “If $\left(a,b\right)$ is a critical point of $f\left(x,y\right)$, all second derivatives of f are continuous, and $f_{xx}\left(a,b\right)=10,f_{yy}\left(a,b\right)=3,f_{xy}\left(a,b\right)=5$, then $\left(a,b\right)$ is a:” from the given options $\left(\text{a}\right)\text{-}\left(\text{d}\right)$.