Let $f(\phi)=\phi^\alpha \phi^\beta -\phi^\alpha $, be a function where $\alpha,\beta\in \mathbb{N}$. Of which domain is the function convex?
I have tried using the Definition for convexity: $(1-\lambda)f(x)+f(y)\leq f((1-\lambda)x+\lambda y)$ and using the method of double differentiation, where $0\leq f''(x)$
But I havent made any real progress, would appreciate some help.