Question

Graph of the position function of two particles are shown , where t is measured in seconds.
when is the particle in figure speeding up ? (enter your answer using interval notations )
when is the particle in the figure slowing down ? (enter your answer using interval notations )

Answer 1

When $\frac{dx}{dt}>0$ , particle is speeding up and when $\frac{dx}{dt}<0$, particle is slowing down ,

So , speeding up for $\to tϵ(0,1)\cup (3,4)$

slowing down for $\to tϵ(1,3)$