Pls comment as I don't have an answer to this exam practice question.

Question.

For the function defined by

,

deduce whether f(x,y) is convex, concave or neither about the point .

Answer.

I will apply the second derivative test:

At the point

and the Hessian matrix looks like this (apologies for the presentation...)

which is a diagonal matrix ->-e and -2 are eigenvalues, and since both are negative, the matrix is negative definite.

Therefore, the function is concave about the point . Is this all to it?