Name: __________________________ Date: _____________

Chapter Review 3 (Part 1)



1.
Find any critical numbers of the function , t < 11.
A.
0
B.
C.
D.
Both A and B
E.
Both A and C


2.
Locate the absolute extrema of the given function on the closed interval [–30,30].

A.
Absolute max: f(5) = 3
B.
Absolute min: f(-5) = –3
C.
No absolute max
D.
No absolute min
E.
Both A and D
F.
Both A and B


3.
Find a function f that has derivative and with graph passing through the point (–6,–2).
A.
B.
C.
D.
E.


4.
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


5.
The graph of f is shown in the figure. Sketch a graph of the derivative of f.

A.


B.


C.


D.


E.




6.
Determine the open intervals on which the graph of is concave downward or concave upward.
A.
Concave downward on ; concave upward on
B.
Concave upward on ; concave downward on
C.
Concave downward on ; concave upward on
D.
Concave upward on ; concave downward on
E.
Concave downward on ; concave upward on


7.
Find the points of inflection and discuss the concavity of the function on the interval .
A.
Concave downward on ; concave upward on . Inflection point at
B.
Concave upward on ; concave downward on . Inflection point at
C.
No inflection points. Concave up on
D.
No inflection points. Concave down on
E.
None of the above


8.
Find all relative extrema of the function . Use the Second Derivative Test where applicable.
A.
Relative min:
B.
Relative max:
C.
No relative max
D.
No relative min
E.
Both A and C
F.
Both B and D


9.
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.




10.
Determine the slant asymptote of the graph of .
A.
No slant asymptotes
B.
C.
D.
E.


11.
Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 169 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


12.
A sector with central angle is cut from a circle of radius 14 inches, and the edges of the sector are brought together to form a cone. Find the magnitude of such that the volume of the cone is a maximum.
A.
radians
B.
radians
C.
radians
D.
radians
E.
radians


13.
Find the differential dy of the function .
A.
B.
C.
D.
E.



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