Optimization problem, minimal speed of point

Question

What is the minimal speed of a point moving according to this law:$$S(t)=t^3+3t+1$$ $[m], t-[s]$
Will I get the answer by finding the global minimum of this function? Or is it about finding a point where function declines the most? I'm lost

Answer 1

If this is the displacement of the particle, we have: $$V(t)=S'(t)=3t^2+3$$ Which is minimal where $t=0$ giving a speed of 3.

If this is the speed of the particle, the speed is minimal at $t=0$ giving a speed of 1.