Playing Carts - II

Consider a Cartesian plane where the functions $f(x) = x^3, \; f'(x), \; f''(x)$ are all plotted.

Let $\triangle{\alpha}$ be the triangle with vertexes on all lattice points for which one of the functions intersects another.

Let $\triangle{\beta}$ be the triangle with vertexes on the first quadrant points for which one of the functions intersects another.

(1) The distance between $\alpha$ 's midpoint to the origin of the Cartesian plane is greater than the one between $\beta$ 's midpoint to the origin.

(2) $\alpha$ contains the greatest side length compared to $\beta$ .

(4) Both triangles are obtuse.

(8) $\alpha$ 's circumradius is greater than $\beta$ 's.

(16) The parabola passing through all $\beta$ 's vertexes has real roots.

Find the sum of the numbers in all correct given statements