Chapter 4.6, Problem 23ES

Let $s\left(t\right)=t/\left(t^2+5\right)$ be the position function of a particle moving along a coordinate line, where s is in meters and $t$ is in seconds. Use a graphing utility to generate the graphs of $s\left(t\right),\upsilon \left(t\right)$ , and $a\left(t\right)$ for $t\ge 0$ , and use those graphs where needed.

(a) Use the appropriate graph to make a rough estimate of the time at which the particle first reverses the direction of its motion; and then find the time exactly.

(b) Find the exact position of the particle when it first reverses the direction of its motion.

(c) Use the appropriate graphs to make a rough estimate of the time intervals on which the particle is speeding up and on which it is slowing down; and then find those time intervals exactly.