I have a function
$a^2 \beta (\beta +1) (\gamma g+1)+a \left(-\beta ^2 (\gamma +1)+\beta \gamma (g-1) (\gamma +\gamma g+2)+(\gamma g+1)^2\right)+(-\gamma -1) (\beta +\gamma +1)$
where
$0 < a <1$
$0 < g <1$
$1 < \beta$
$ 1 < \gamma$
I am trying to determine if it is strictly concave, convex or not.
Is this the correct procedure? 1) Determine Hessian 2) Determine Eigenvalues 3) if all eigenvalues positive -> strictly convex, all negative -> strictly concave, otherwise neither
I am unclear about how to pick the values with which to compute eigenvalues?