I have two questions about convexity:
f(x,y) is a convex function,
are the following functions convex too?
I don`t really understand how to answer to this, in my opinion it is clear that they remain convex, but I'm not sure about the correct explaination why.
Is f(x,y)=ln(1-(x-a)2-y2) convex or concave?
"a" stands for a real number.
Can I simply perform the second derivative test on this?
So I set f`(x,y)=0 to get stationary points, than I take the second derivative and fill in the stationary points in order to test for convexity?