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?