Chapter 4, Problem 67RE

For parts (a)-(f), suppose that the position function of a particle in rectilinear motion is given by the formula $s\left(t\right)=\frac{t^2+1}{t^4+1},t\ge 0$

(a) Use a CAS to find simplified formulas for the velocity function $\upsilon \left(t\right)$ and the acceleration function $a\left(t\right)$ .

(b) Graph the position, velocity, and acceleration versus time curves.

(c) Use the appropriate graph to make a rough estimate of the time at which the particle is farthest from the origin and its distance from the origin at that time.

(d) Use the appropriate graph to make a rough estimate of the time interval during which the particle is moving in the positive direction.

(e) Use the appropriate graphs to make rough estimates of the time intervals during which the particle is speeding up and the time intervals during which it is slowing down.

(f) Use the appropriate graph to make a rough estimate of the maximum speed of the particle and the time at which the maximum speed occurs.