Looking to find and classify critical points:
subject to constraint:
So, let
which gives:
which gives:
Thus:
And I'm stuck...
...then you continue! Cross multiply and get: 2x^2 + 3yx - 2y^2 = 0 . This is a quadratic in x, and solving it we get 2(x + 2y)(x - y/2) = 0 ==> input these solutions for x now in g(x,y) and find y, and then x. I thinbk there are 4 different points, two of which are (2,4) and (-2, -4)...check this, though! I could easily be wrong...
Tonio