Discussion
For \( f(x,y) = xy \) the origin is
Answer: B
Both first derivatives vanish at the origin, since \( f_{x} = y \) and \( f_{y} = x \). The second derivatives give \( f_{xx} = f_{yy} = 0 \) and \( f_{xy} = 1 \), so
\[ D \;=\; (0)(0) - 1^{2} \;=\; -1 \;<\; 0, \]
which is the saddle condition. The surface rises along \( y = x \) and falls along \( y = -x \)
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