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Calculus I
2007 Paul Dawkins 1
http://tutorial.math.lamar.edu/terms.aspx
PrefaceHere are a set of problems for my Calculus I notes. These
problems do not have any solutions
available on this site. These are intended mostly for
instructors who might want a set of problems
to assign for turning in. I try to put up both practice problems
(with solutions available) and these
problems at the same time so that both will be available to
anyone who wishes to use them.
As with the set of practice problems I write these as I get the
time and some sections will have
only a few problems at this point and others wont have any
problems in them yet. Rest assured
that Im always trying to get more problems written but this site
has been written and maintained
in my spare time and so I usually cannot devote as much time as
Id like to the site.
ProductandQuotientRuleFor problems 1 7 use the Product Rule or
the Quotient Rule to find the derivative of the given
function.
1. ( ) ( )( )3 22 3 8h z z z = - +
2. ( ) ( )32 7 2f x x xx = - -
3. ( )( )2 35 1 12 2y x x x x= - + + -
4. ( )3
21
xg x
x=
+
5. ( )2
4
6
y yZ y
y
-=
-
6. ( )2
3
1 10
5 2
t tV t
t t
- +=
+
7. ( )( )( )1 4 2
3 9
w wf w
w
- +=
+
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Calculus I
2007 Paul Dawkins 2
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For problems 8 12 use the fact that ( )3 12f - = , ( )3 9f - = ,
( )3 4g - = - , ( )3 7g - = ,
( )3 2h - = - and ( )3 5h - = determine the value of the
indicated derivative.
8. ( ) ( )3f g -
9. ( )3h
g
-
10. ( )3f g
h
-
11. If ( ) ( )x f x h x= - determine3x
dy
dx =-.
12. If( ) ( )
( )
1 g x h xy
f x
-=
+determine
3x
dy
dx =-.
13. Find the equation of the tangent line to ( ) ( )( )2 28 1f x
x x x= - + + at 2x = - .
14. Find the equation of the tangent line to ( )3
24 2xf xx
-= +
at 1= .
15. Determine where ( )2
2
12
zg z
z
-=
+is increasing and decreasing.
16. Determine where ( ) ( )( )23 1 2R x x x x= - - + is
increasing and decreasing.
17. Determine where ( )2
2
7
1 2
t th t
t
-=
+is increasing and decreasing.
18. Determine where ( )1
1f x
+=
-is increasing and decreasing.
19. Using the Product Rule for two functions prove the Product
Rule for three functions.
( )f g h f g h f g h f g h = + +
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Calculus I
2007 Paul Dawkins 3
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