Let f(x,y) = 3x²-2y²+y+x-2y+1. Find all critical points, and state what type they are. Note: Many textbook examples and problems about critical points for functions of two variables involve quadratic functions. Actually, that's a bit of an overkill, since for these functions (historically called "conic sections"), you don't really need calculus to determine their minima, maxima or saddle points: in fact the tools we use for general functions of two variables rely on the non-calculus results for quadratic functions. However, a little com- plications like this one makes the difficulty level only marginally higher. Just apply the tools and it should work out easily.

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