Question

Let f(x,y) = 3x^2y − 2y^2 − 3x^2 − 8y + 2. (i) Find the stationary...

Let f(x,y) = 3x^2y − 2y^2 − 3x^2 − 8y + 2.

(i) Find the stationary points of f.

(ii) For each stationary point P found in (i), determine whether f has a local maximum, a local minimum, or a saddle point at P.

Answer:

(i) (0, −2), (2, 1), (−2, 1)

(ii) (0, −2) loc. max, (± 2, 1) saddle points

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