Question

The level curves of a function f(x, y) consist of a collection of hyperbolas and two lines. If the lines intersect at a point P, what are the possibilities for P? Type the letters of all possibilities, with no punctuation, in alphabetical order.

A. P is a local maximum, that is, f(P) ≥ f(Q) for all Q near P.

B. P is a local minimum, that is, f(P) ≤ f(Q) for all Q near P.

C. P is neither a local maximum nor a local minimum.