One popular model for the interactions between two molecules is the Leonard-Jones 6-3 potential.

According to this model, the energy of interaction between two molecules that are distance r apart is given by the following function.

V(r) = 1/r^6 - A/r^3, r>0

Molecules will attract or repel each other until they reach a distance that minimizes the function V(r). A is a positive constant. Find the value of r that minimizes V (r).

A train moves along a straight line. Its location at time t is given by s(t) = 5, 3 < t 8, where t is measured in hours and s(t) is measured in kilometers. Find the average velocity of the train between t = 3 and t = 8.