Larson_Calculus_10e ch03sec03
MULTIPLE CHOICE
1. Use the graph of the function given below to estimate the open intervals on which the
function is increasing or decreasing.
a.
increasing on ; decreasing on
b.
increasing on ; decreasing on
c.
increasing on ; decreasing on
d.
increasing on ; decreasing on
e.
increasing on ; decreasing on
2. Identify the open intervals where the function is increasing or decreasing.
a.
decreasing on
b.
increasing on
c.
d.
decreasing on ; increasing on
e.
3. Identify the open intervals where the function is increasing or decreasing.
a.
decreasing: ; increasing:
b.
decreasing on
c.
increasing: ; decreasing:
d.
increasing: ; decreasing:
e.
increasing: ; decreasing:
4. Identify the open intervals on which the function is increasing or
decreasing.
a.
increasing on decreasing on
b.
increasing on decreasing on
c.
increasing on decreasing on
d.
increasing on decreasing on
e.
increasing on decreasing on
5. Find the critical number of the function .
a.
b.
c.
d.
e.
6. Find the open interval(s) on which is increasing or decreasing.
a.
increasing on decreasing on
b.
increasing on decreasing on
c.
increasing on decreasing on
d.
increasing on decreasing on
e.
increasing on decreasing on
7. Find the relative extremum of by applying the First Derivative Test.
a.
relative minimum:
b.
relative maximum:
c.
relative minimum:
d.
relative minimum:
e.
relative maximum:
8. 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 ,
(b) increasing: ; decreasing:
(c) relative max: ; relative min:
b.
(a) x = 0 ,
(b) decreasing: ; increasing:
(c) relative min: ; relative max:
c.
(a) x = 0 ,
(b) increasing: ; decreasing:
(c) relative max: ; no relative min.
d.
(a) x = 0 ,
(b) increasing: ; decreasing:
(c) relative max: ; relative min:
e.
(a) x = 0 ,
(b) decreasing: ; increasing:
(c) relative min: ; relative max:
9. 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.
Use a graphing utility to confirm your results.
a.
(a)
(b) increasing: ; decreasing:
(c) relative max:
b.
(a)
(b) increasing: ; decreasing:
(c) relative max:
c.
(a)
(b) decreasing: ; increasing:
(c) relative min:
d.
(a)
(b) decreasing: ; increasing:
(c) relative min: ; relative max:
e.
(a)
(b) decreasing: ; increasing:
(c) relative min:
10. Find the open interval(s) on which the function is increasing in the interval
Round numerical values in your answer to three decimal places.
a.
increasing on:
b.
increasing on:
c.
increasing on:
d.
increasing on:
e.
increasing on:
11. Find the open interval(s) on which the function is increasing in the interval
Round numerical values in your answer to three decimal places.
a.
increasing on:
b.
increasing on:
c.
increasing on:
d.
increasing on:
e.
increasing on:
12. Find the relative maxima of on the interval by applying the First
Derivative Test. Round numerical values in your answer to three decimal places.
a.
relative maxima:
b.
relative maxima:
c.
relative maxima:
d.
relative maxima:
e.
relative maxima:
13. Find the relative minima of on the interval by applying the First
Derivative Test. Round numerical values in your answer to three decimal places.
a.
relative minima:
b.
relative minima:
c.
relative minima:
d.
relative minima:
e.
relative minima:
14. The graph of f is shown in the figure. Sketch a graph of the derivative of f.
a.
d.
b.
e.
The derivative of f does not exist.
c.
15. The graph of f is shown in the figure. Sketch a graph of the derivative of f.
a.
d.
b.
e.
c.
16. The graph of f is shown in the figure. Sketch a graph of the derivative of f.
a.
d.
b.
e.
c.
17. The graph of f is shown in the figure. Sketch a graph of the derivative of f.
a.
d.
b.
e.
c.
18. A ball bearing is placed on an inclined plane and begins to roll. The angle of elevation of the
plane is radians. The distance (in meters) the ball bearing rolls in t seconds is
. Determine the speed of the ball bearing after t seconds.
a.
speed: meters per second
b.
speed: meters per second
c.
speed: meters per second
d.
speed: meters per second
e.
speed: meters per second
19. A ball bearing is placed on an inclined plane and begins to roll. The angle of elevation of the
plane is radians. The distance (in meters) the ball bearing rolls in t seconds is
. Determine the value of after one second. Round numerical values in
your answer to one decimal place.
a.
b.
c.
d.
e.
20. The resistance R of a certain type of resistor is where R is measured in
ohms and the temperature T is measured in degrees Celsius. Use a computer algebra system to find
a.
b.
c.
d.
e.
21. The resistance R of a certain type of resistor is where R is measured in
ohms and the temperature T is measured in degrees Celsius. Use a computer algebra system to find the
critical number of the function. Round numerical values in your answer to the nearest whole number.
a.
b.
c.
d.
e.
22. The resistance R of a certain type of resistor is where R is measured in
ohms and the temperature T is measured in degrees Celsius. Use a computer algebra system to
determine the minimum resistance for this type of resistor. Round your answer to two decimal places.
a.
b.
c.
d.
e.