TMUA 2018 Paper 2 Question 18

$\mathrm{f}(x)$ is a polynomial function defined for all real $x$. Which of the following is a necessary condition for the inequality $$\frac{\mathrm{f}(a)+\mathrm{f}(b)}{2}\ge \mathrm{f}\left(\frac{a+b}{2}\right)$$ to be true for all real numbers $a$ and $b$ with $a<b$?