Math 1210-001
Homework 3
Due 10 June, 2013
This homework assignment is designed to go along with sections 2.3 through
2.6 of your textbook, which we have completed in class. The majority of
your score will be based on how you organize and demonstrate the process of
solving each problem. To that end, make sure your work is neat, legible,
well-organized and self-explanatory. You must staple your assignment to
receive full credit.
Name:
1. (10 points) Use the Product Rule to show that
Dx (f (x))2 = 2 · f (x) · Dx f (x).
Note: This can be shown with the chain rule, but you should use the product rule
instead.
2. (10 points) At time t seconds, the center of a bobbing cork is h(t) = 3 sin(2t) centimeters
above (or below) the water level. What is the instantaneous velocity of the cork at times
t = 0, π2 , and π seconds?
Solution: h0 (t) = 6 cos(2t)
h0 (0) = 6, h0 (π/2) = −6, h0 (π) = 6 cm per second.
3. (10 points) Use the Chain Rule to find
u+1
4
Du cos
u−1
Hint: You need to apply the Chain Rule more than once!
Solution:
Du cos4
u+1
u−1
=8
cos3
u+1
u−1
sin
(u − 1)2
u+1
u−1
4. (10 points) An object moves along a horizontal coordinate line in such a way that its
3
position at time t is specified by s = t3 − 3t2 − 24t − 6. Find ddt3s .
Solution:
ds
= 3t2 − 6t − 24
dt
d2 s
= 6t − 6
dt2
d3 s
=6
dt3
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