Discussion
For \( f(x,y) \) with \( f_{x} = f_{y} = 0 \) at a point, write \( D = f_{xx}f_{yy} - f_{xy}^{2} \). A minimum is indicated by
Answer: D
A positive discriminant means the surface curves the same way in every direction, and the sign of \( f_{xx} \) then says which way: positive for a minimum, negative for a maximum. A negative \( D \) gives a saddle, curving up one way and down another, and \( D = 0 \) leaves the test with nothing to say
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