Discussion
The Taylor expansion of \( f(x,y) \) about \( (a,b) \) has first-order terms
Answer: B
Each first derivative is weighted by the increment of its own variable, so the linear part is
\[ f(a,b) + (x-a)f_{x}(a,b) + (y-b)f_{y}(a,b). \]
This is the tangent plane to the surface at the point. The pairing that crosses the two derivatives attaches each to the wrong increment, and the term in \\( f_{xy} \\) belongs to the second-order group
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