How would you work out when this function turns and goes in a different direction? (like a turning point for a parabola):

Question

s=0.2t(t-5.1)(t-9.1)

Answer 1

it will be halfway between the roots, or
turning point is when tis halfway between 5.1 and 9.1, or t=7.1. Put that into the s equation, and solve.

Answer 2

since it's a cubic, it's hard to do without calculus.

The easiest way is to examine its graph.

http://www.wolframalpha.com/input/?i=0.2t%28t-5.1%29%28t-9.1%29

Looks like t≈2.1 or 7.4