Find the derivatives of the following functions three different
ways using Maple. From the definition, using the D command, and
using the diff command. Note that Maple has its own ideas of
what form the answer should take, so some of your answers may look
unfamiliar or be more complicated than you think they should.
Determine the derivative of the function f(x) defined by
for all values of x for which f'(x) exists. Describe how you
obtained your results.
Suppose that s(t), defined as
for , describes motion of a particle in one
dimension. That is, s is the distance of the particle from some
reference point as a function of time.
Find the secant line of the graph of s between t=1 and
Describe how you can use your answer to the first part of this
exercise to compute the average velocity of the particle over the time
interval . Report the value of the average velocity.