James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

Section 2.8 The Derivative as a Function 163
36. The table gives the number Nstd, measured in thousands, of
minimally invasive cosmetic surgery procedures performed
in the United States for various years t.
t Nstd (thousands)
2000 5,500
2002 4,897
2004 7,470
2006 9,138
2008 10,897
2010 11,561
2012 13,035
40. Suppose N is the number of people in the United States who
travel by car to another state for a vacation this year when
the average price of gasoline is p dollars per gallon. Do you
expect dNydp to be positive or negative? Explain.
41–44 The graph of f is given. State, with reasons, the numbers
at which f is not differentiable.
41.
y
_2 0 2 x
42.
_2
y
2 4 x
Source: American Society of Plastic Surgeons
(a) What is the meaning of N9std? What are its units?
(b) Construct a table of estimated values for N9std.
(c) Graph N and N9.
(d) How would it be possible to get more accurate values
for N9std?
43.
y
0
2 4 6 x
44.
y
_2 0 2 4 x
37. The table gives the height as time passes of a typical pine
tree grown for lumber at a managed site.
Tree age (years) 14 21 28 35 42 49
Height (feet) 41 54 64 72 78 83
Source: Arkansas Forestry Commission
If Hstd is the height of the tree after t years, construct a table
of estimated values for H9 and sketch its graph.
38. Water temperature affects the growth rate of brook trout.
The table shows the amount of weight gained by brook trout
after 24 days in various water temperatures.
Temperature (°C) 15.5 17.7 20.0 22.4 24.4
;
;
45. Graph the function f sxd − x 1 s| x | . Zoom in repeatedly,
first toward the point (21, 0) and then toward the origin.
What is different about the behavior of f in the vicinity of
these two points? What do you conclude about the differentiability
of f ?
46. Zoom in toward the points (1, 0), (0, 1), and (21, 0) on
the graph of the function tsxd − sx 2 2 1d 2y3 . What do you
notice? Account for what you see in terms of the differentiability
of t.
47–48 The graphs of a function f and its derivative f 9 are
shown. Which is bigger, f 9s21d or f 99s1d?
Weight gained (g) 37.2 31.0 19.8 9.7 29.8
47.
y
If Wsxd is the weight gain at temperature x, construct a table
of estimated values for W9 and sketch its graph. What are
the units for W9sxd?
0
1
x
Source: Adapted from J. Chadwick Jr., “Temperature Effects on Growth
and Stress Physiology of Brook Trout: Implications for Climate Change
Impacts on an Iconic Cold-Water Fish.” Masters Theses. Paper 897. 2012.
scholarworks.umass.edu/theses/897.
39. Let P represent the percentage of a city’s electrical power
that is produced by solar panels t years after January 1, 2000.
(a) What does dPydt represent in this context?
(b) Interpret the statement
dP
dt
Z − 3.5
t −2
48.
y
1 x
Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.