Is there some kind of trick to defining the domain of the concavity/convexity (if it exists)? I have no idea how to work with the resultant hessian
2026-03-25 06:03:50.1774418630
Is $z = x^2y^3(1-x-y)$ convex or concave?
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Easy to see that we can not say that $$\frac{\partial^2(x^2y^3(1-x-y))}{\partial x^2}\geq0$$ for all reals $x$ and $y$ and we can not say that $$\frac{\partial^2(x^2y^3(1-x-y))}{\partial x^2}\leq0$$ for all reals $x$ and $y$.
What does follow from this?