The position of a body moving along the s-axis is s=1/3t^3 - 2t^2 + 3t. When is the body's velocity increasing? Decreasing?

Answer 1

v(t) = s'(t) = t^2 -4t +3= 0

(t-3)(t-1)= 0

t=1 and 3 are the end points of intervals where velocity changes direction

v increases in the intervals (-inf, 1,)U(3,inf)

decreases in (1,3)