Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
Q19 needed ASAP
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![10.
11.
12.
1
A
13. Describe the way the slope changes as you move along the
graph (from left to right) in Exercise 5.
14. Describe the way the slope changes on the graph in Exercise 6.
15. Describe the way the slope changes on the graph in Exercise 8.
16. Describe the way the slope changes on the graph in Exercise 10.
Exercises 17 and 18 refer to the graph in Fig. 20.
A
B
с.
y = f(x)
qmD RE
Figure 20
17. (a) At which labeled points is the function increasing?
(b) At which labeled points is the graph concave up?
(c) Which labeled point has the most positive slope?
18. (a) At which labeled points is the function decreasing?
(b) At which labeled points is the graph concave down?
2.1 Describing Graphs of Functions. 139
(c) Which labeled point has the most negative slope (that is,
negative and with the greatest magnitude)?
In Exercises 19-22, draw the graph of a function y=f(x) with the
stated properties.
19. Both the function and the slope increase as x increases.
20. The function increases and the slope decreases as x increases.
21. The function decreases and the slope increases as x increases.
[Note: The slope is negative but becomes less negative.]
22. Both the function and the slope decrease as x increases. [Note:
The slope is negative and becomes more negative.]
23. Annual World Consumption of Oil The annual world consump-
tion of oil rises each year. Furthermore, the amount of the annual
increase in oil consumption
graph that could represent the annual world consumption of oil.
also rising each year. Sketch a
24. Average Annual Income In certain professions, the average
annual income has been rising at an increasing rate. Let f(T)
denote the average annual income at year T for persons in one of
these professions and sketch a graph that could represent f(T).
25. A Patient's Temperature At noon, a child's temperature is
101°F and is rising at an increasing rate. At 1 P.M. the child is
given medicine. After 2 P.M. the temperature is still increasing
but at a decreasing rate. The temperature reaches a peak of 103°
at 3 P.M. and decreases to 100° by 5 P.M. Draw a possible graph
of the function 7(1), the child's temperature at time t.
26. A Cost Function Let C(x) denote the total cost of manufactur-
ing x units of some product. Then C(x) is an increasing func-
tion for all x. For small values of x, the rate of increase of C(x)
decreases (because of the savings that are possible with "mass
production"). Eventually, however, for large values of x, the
cost C(x) increases at an increasing rate. (This happens when
production facilities are strained and become less efficient.)
Sketch a graph that could represent C(x).
27. Blood Flow through the Brain One method of determining the
level of blood flow through the brain requires the person to
inhale air containing a fixed concentration of N₂O, nitrous
oxide. During the first minute, the concentration of N₂0 in
the jugular vein grows at an increasing rate to a level of .25%.
Thereafter, it grows at a decreasing rate and reaches a concen-
tration of about 4% after 10 minutes. Draw a possible graph
of the concentration of N₂O in the vein as a function of time.
28. Pollution Suppose that some organic waste products are
dumped into a lake at time r = 0 and that the oxygen content
of the lake at time t is given by the graph in Fig. 21. Describe
the graph in ysical terms. Indicate the significance of the
inflection point at t = b.
Oxygen content of water
b
Time (days)
Figure 21 A lake's recovery from pollution.
a](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F638d3a15-e6c8-4dbb-af03-e006d7a575bc%2Fd2da8134-27c1-4040-b4e5-f07d4b5b8124%2Fv5vvzkm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:10.
11.
12.
1
A
13. Describe the way the slope changes as you move along the
graph (from left to right) in Exercise 5.
14. Describe the way the slope changes on the graph in Exercise 6.
15. Describe the way the slope changes on the graph in Exercise 8.
16. Describe the way the slope changes on the graph in Exercise 10.
Exercises 17 and 18 refer to the graph in Fig. 20.
A
B
с.
y = f(x)
qmD RE
Figure 20
17. (a) At which labeled points is the function increasing?
(b) At which labeled points is the graph concave up?
(c) Which labeled point has the most positive slope?
18. (a) At which labeled points is the function decreasing?
(b) At which labeled points is the graph concave down?
2.1 Describing Graphs of Functions. 139
(c) Which labeled point has the most negative slope (that is,
negative and with the greatest magnitude)?
In Exercises 19-22, draw the graph of a function y=f(x) with the
stated properties.
19. Both the function and the slope increase as x increases.
20. The function increases and the slope decreases as x increases.
21. The function decreases and the slope increases as x increases.
[Note: The slope is negative but becomes less negative.]
22. Both the function and the slope decrease as x increases. [Note:
The slope is negative and becomes more negative.]
23. Annual World Consumption of Oil The annual world consump-
tion of oil rises each year. Furthermore, the amount of the annual
increase in oil consumption
graph that could represent the annual world consumption of oil.
also rising each year. Sketch a
24. Average Annual Income In certain professions, the average
annual income has been rising at an increasing rate. Let f(T)
denote the average annual income at year T for persons in one of
these professions and sketch a graph that could represent f(T).
25. A Patient's Temperature At noon, a child's temperature is
101°F and is rising at an increasing rate. At 1 P.M. the child is
given medicine. After 2 P.M. the temperature is still increasing
but at a decreasing rate. The temperature reaches a peak of 103°
at 3 P.M. and decreases to 100° by 5 P.M. Draw a possible graph
of the function 7(1), the child's temperature at time t.
26. A Cost Function Let C(x) denote the total cost of manufactur-
ing x units of some product. Then C(x) is an increasing func-
tion for all x. For small values of x, the rate of increase of C(x)
decreases (because of the savings that are possible with "mass
production"). Eventually, however, for large values of x, the
cost C(x) increases at an increasing rate. (This happens when
production facilities are strained and become less efficient.)
Sketch a graph that could represent C(x).
27. Blood Flow through the Brain One method of determining the
level of blood flow through the brain requires the person to
inhale air containing a fixed concentration of N₂O, nitrous
oxide. During the first minute, the concentration of N₂0 in
the jugular vein grows at an increasing rate to a level of .25%.
Thereafter, it grows at a decreasing rate and reaches a concen-
tration of about 4% after 10 minutes. Draw a possible graph
of the concentration of N₂O in the vein as a function of time.
28. Pollution Suppose that some organic waste products are
dumped into a lake at time r = 0 and that the oxygen content
of the lake at time t is given by the graph in Fig. 21. Describe
the graph in ysical terms. Indicate the significance of the
inflection point at t = b.
Oxygen content of water
b
Time (days)
Figure 21 A lake's recovery from pollution.
a
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