Exercises 2.2

1. A mass is attached to a certain spring which has a motor attached. The displacement x(t) in centimeters at time t seconds is given by

.

(a) Make a MapleV plot of the the displacement as a function of t over the interval [0,2].

(b) Determine the time or times when displacement is a maximum.

(c) At what time is x(t) increasing at its fastest? When is x(t) decreasing the fastest?

2. Show that is an increasing function for every interval.

3. Show that ) is an increasing function for every interval.

4. Show that , if .