Convexity of the surface $x^2+z^2-y^3(1-y)^3 = 0$

Question

I am working on the following exercise:

Consider the surface $F$ given by $$F= \left\{ (x,y,z) \in \mathbb{R}^3 \colon x^2+z^2-y^3(1-y)^3 = 0 \right\}$$ For which points on the surface is $F$ convex?

REMARK: The surface looks like this one here:

I would say that from the graphic it is obvious that $F$ is not convex, because it cannot contain a line segment of two points due to its roundness. But the part of the question "For which points on the surface" confuses me. What is meant by that?