The Mixed Partial Derivative Theorem allows us to write D\displaystyle {D} (in the the Second Derivative Test) as either
D(x,y)=(fxx)(fyy)(fxy)2\displaystyle {D}{\left({x},{y}\right)}={\left({f}_{{{x}{x}}}\right)}{\left({f}_{{{y}{y}}}\right)}-{\left({f}_{{{x}{y}}}\right)}^{{2}}
or
D(x,y)=(fxx)(fyy)(fyx)2\displaystyle {D}{\left({x},{y}\right)}={\left({f}_{{{x}{x}}}\right)}{\left({f}_{{{y}{y}}}\right)}-{\left({f}_{{{y}{x}}}\right)}^{{2}}.