Name: __________________________ Date: _____________



1.
Find the value of the derivative (if it exists) of the function at the extremum point (0,6).
A.
0
B.
Does not exist
C.
6
D.
–6
E.
None of the above


2.
Find the value of the derivative (if it exists) of the function at the extremum point (0,0).
A.
0
B.
1
C.
-1
D.
E.


3.
Find any critical numbers of the function , t < 13.
A.
0
B.
C.
D.
Both A and B
E.
Both A and C


4.
Find any critical numbers of of the function , .
A.
B.
C.
D.
E.
Both A and B
F.
Both A and C


5.
Locate the absolute extrema of the function on the closed interval .
A.
No absolute max; Absolute min: f(–1) = 3
B.
Absolute max: f(2) = –6 ; Absolute min: f(–1) = 3
C.
Absolute max: f(–1) = 3 ; No absolute min
D.
Absolute max: f(–1) = 3 ; Absolute min: f(2) = –6
E.
No absolute max or min


6.
Locate the absolute extrema of the function on the closed interval [0,7].
A.
Absolute max: f(7) = 7 ; Absolute min: f(4) = –128
B.
Absolute max: f(4) = –128 ; Absolute min: f(7) = 7
C.
Absolute max: f(7) = 7 ; No absolute min
D.
No absolute max; Absolute min: f(7) = 7
E.
No absolute max or min


7.
Determine whether Rolle's Theorem can be applied to the function on the closed interval .
If Rolle's Theorem can be applied, find all numbers c in the open interval such that .
A.
Rolle's Theorem applies; 1
B.
Rolle's Theorem applies; 2
C.
Rolle's Theorem applies; 0
D.
Rolle's Theorem applies: 0.5
E.
Rolle's Theorem does not apply


8.
Determine whether the Mean Value Theorem can be applied to the function on the closed interval [1,9]. If the Mean Value Theorem can be applied, find all numbers c in the open interval (1,9) such that .
A.
MVT applies; 4
B.
MVT applies; 6
C.
MVT applies; 5
D.
MVT applies; 7
E.
MVT applies; 3


9.
Identify the open intervals where the function is increasing or decreasing.
A.
Decreasing: ; Increasing:
B.
Increasing: ; Decreasing:
C.
Increasing: ; Decreasing:
D.
Increasing: ; Decreasing:
E.
Decreasing for all x


10.
For the function :

(a) Find the critical numbers of f (if any);
(b) Find the open intervals where the function is increasing or decreasing; and
(c) Apply the First Derivative Test to identify all relative extrema.

Then use a graphing utility to confirm your results.
A.
(a) x = 0 , 7
(b) Increasing: ; Decreasing:
(c) Relative max: ; Relative min:
B.
(a) x = 0 , 7
(b) Decreasing: ; Increasing:
(c) Relative min: ; Relative max:
C.
(a) x = 0 , 2
(b) Increasing: ; Decreasing:
(c) Relative max: ; Relative min:
D.
(a) x = 0 , 2
(b) Decreasing: ; Increasing:
(c) Relative min: ; Relative max:
E.
(a) x = 0 , 2
(b) Increasing: ; Decreasing:
(c) Relative max: ; No relative min.


11.
Consider the function on the interval .

(a) Find the critical points of the function;
(b) Find the open intervals where the function is increasing or decreasing; and
(c) Apply the First Derivative Test to identify all relative extrema.

Use a graphing utility to confirm your results.
A.
(a)
(b) Decreasing: ; Increasing:
(c) Relative min at
B.
(a)
(b) Increasing: ; Decreasing:
(c) Relative min at ; Relative max at
C.
(a)
(b) Decreasing: ; Increasing:
(c) Relative max at ; Relative min at
D.
(a)
(b) Decreasing: ; Increasing:
(c) Relative min at
E.
(a)
(b) Increasing: ; Decreasing:
(c) Relative max at


12.
The graph of f is shown in the figure. Sketch a graph of the derivative of f.

A.


B.


C.


D.


E.




13.
The graph of f is shown in the figure. Sketch a graph of the derivative of f.

A.


B.


C.


D.


E.




14.
The graph of f is shown in the figure. Sketch a graph of the derivative of f.

A.


B.


C.


D.


E.




15.
The graph of f is shown in the figure. Sketch a graph of the derivative of f.

A.


B.
The derivative of f does not exist.
C.


D.


E.




16.
Determine the open intervals on which the graph of is concave downward or concave upward.
A.
Concave downward on
B.
Concave downward on ; concave upward on
C.
Concave upward on ; concave downward on
D.
Concave downward on ; concave upward on
E.
Concave upward on ; concave downward on


17.
Determine the open intervals on which the graph of is concave downward or concave upward.
A.
Concave upward on ; concave downward on
B.
Concave downward on
C.
Concave upward on
D.
Concave downward on ; concave upward on
E.
Concave upward on ; concave downward on


18.
Find the points of inflection and discuss the concavity of the function .
A.
Inflection point at x = 10. Concave down on
B.
No inflection points. Concave down on
C.
Inflection point at x = 10. Concave up on
D.
No inflection points. Concave up on
E.
Inflection point at x = 0. Concave up on ; concave down on


19.
Match the function with one of the following graphs.
A.

B.

C.

D.

E.



20.
Match the function with one of the following graphs.
A.

B.

C.

D.

E.



21.
Match the function with one of the following graphs.
A.

B.

C.

D.

E.



22.
For the function , use a graphing utility to complete the table and estimate the limit as x approaches infinity.
x
100
101
102
103
104
105
106
f(x)
 
 
 
 
 
 
 
 
A.
–5
B.
–0.2
C.
0.8
D.
–4
E.
–6


23.
Find the limit.
A.
B.
C.
1
D.
0
E.
Does not exist


24.
Find the limit.
A.
3
B.
C.
D.
1
E.


25.
Sketch the graph of the function using any extrema, intercepts, symmetry, and asymptotes.
A.


B.


C.


D.


E.




26.
Sketch the graph of the function using any extrema, intercepts, symmetry, and asymptotes.
A.


B.


C.


D.


E.




27.
Sketch the graph of the relation using any extrema, intercepts, symmetry, and asymptotes.
A.

B.

C.

D.

E.



28.
The graph of a function f is is shown below:



Which of the following graphs is the graph of its derivative ?
A.


B.


C.


D.


E.




29.
The graph of a function f is is shown below:



Which of the following graphs is the graph of its derivative '?
A.


B.


C.


D.


E.




30.
The graph of a function f is is shown below:



Which of the following graphs is the graph of its derivative ?
A.


B.


C.


D.


E.




31.
The graph of f is shown in the figure.



Which of the following is correct?
A.
is        is
B.
is        is
C.
is        is
D.
is        is
E.
None of the above


32.
Analyze and sketch a graph of the function .
A.


B.


C.


D.


E.




33.
Analyze and sketch a graph of the function .
A.


B.


C.


D.


E.




34.
Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 361 meters.
A.
Square base side ; height
B.
Square base side ; height
C.
Square base side ; height
D.
Square base side ; height
E.
Square base side ; height


35.
Use Newton's Method toapproximate the zero(s) of the function accurate to three decimal places.
A.
–0.473
B.
0.474
C.
0.473
D.
–0.475
E.
0.47


36.
Compare dy and for at x = 1 with dx = –0.09. Give your answers to four decimal places.
A.
dy = –0.3400 ; = –0.3146
B.
dy = –0.3700 ; = –0.3145
C.
dy = –0.3900 ; = –0.3144
D.
dy = –0.3600 ; = –0.3143
E.
dy = –0.3400 ; = –0.3144


37.
Find the differential dy of the function .
A.
B.
C.
D.
E.



STOP This is the end of the test. When you have completed all the questions and reviewed your answers, press the button below to grade the test.