I have a function of which I have identified a series of critical point.
$f(x,y)=y^2+\sin(y)$
The partial derivates
$A = \dfrac{d}{dxdx}f(x,y)=0 $
$B = \dfrac{d}{dxdy}f(x,y)=0 $
$C = \dfrac{d}{dydy}f(x,y)=2y+\cos(y)$
This gives me a series of critical points at $(x,-0.45)$
I don't know how to analytical answer if those are saddle points, minimum or maximum as the formula $B^2-A*C = 0 = $no information.
However using numerical computer programs I can see that it is a minimum point. However I don't know if this is an acceptable approached in univeristy?