Let f(x,y) = 3x3 + 3x2 y − y3 −
15x.
a) Find and classify the critical points of f. Use any method
taught during the course (the second-derivative test or completing
the square).
b) One of the critical points is (a,b) = (1,1). Write down the
second-degree Taylor approximation of f about this point and
motivate, both with computations and with words, how one can see
from this approximation what kind of critical point (1,1) is. Use
completing the...