Question 42
Find all functions $f: \mathbb{R}_{\geq 0} \rightarrow \mathbb{R}$ that satisfy
$$
2 x^{3} z f(z)+y f(y) \geq 3 y z^{2} f(x)
$$
for all $x, y, z \in \mathbb{R}_{\geq 0}$.
$$
2 x^{3} z f(z)+y f(y) \geq 3 y z^{2} f(x)
$$
for all $x, y, z \in \mathbb{R}_{\geq 0}$.