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  3. let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a

Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the critical...

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Basic Math

Let f(x,y) = 3x3 + 3x2 y − y3 −15x.

a) Find and classify the critical points of f. Use any methodtaught during the course (the second-derivative test or completingthe square).

b) One of the critical points is (a,b) = (1,1). Write down thesecond-degree Taylor approximation of f about this point andmotivate, both with computations and with words, how one can seefrom this approximation what kind of critical point (1,1) is. Usecompleting the square.

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