TMUA 2018 · Paper 2 · Question 18

$f (x)$ is a polynomial function defined for all real $x$ .

Which of the following is a necessary condition for the inequality

\frac{f ( a ) + f ( b )}{2} \geq f (\frac{a + b}{2})

to be true for all real numbers $a$ and $b$ with $a < b$ ?