Problem

Source: Romania National Olympiad 2022

Tags: romania, calculus, function, Functional inequality



Determine all functions $f:\mathbb{R}\to\mathbb{R}$ which are differentiable in $0$ and satisfy the following inequality for all real numbers $x,y$ \[f(x+y)+f(xy)\geq f(x)+f(y).\]Dan Ștefan Marinescu and Mihai Piticari