Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
Related questions
Question
Question 24
Transcribed Image Text:22. y = 1, y = -1 are horizontal asymptotes
tion provides a good fit to the data:
3
3
and for x >
2
f is increasing for x < -
58.7(х — 0.03)
2
f(x) =
wolves per 1000 km²
0.76+ x
f is decreasing for –1 < x < 1
where x is number of moose per square kilometer.
graph is concave down for x < –1 and for 0 < x < 1
a. Find the horizontal and vertical asymptotes.
graph is concave up for x > 1 and for –1 < x < 0
b. Determine on which intervals f is increasing and
decreasing.
Level 2 APPLIED AND THEORY PROBLEMS
c. Determine on which intervals f is concave up
23. Consider the graph of y = ax² + bx +c for
constants a, b, and c. Use second derivatives
to determine what happens to the graph as a
changes.
and concave down.
d. Use the information from parts a-c to sketch the
graph of f(x).
30. Two mathematicians, W. O. Kermack and A. G.
McKendrick, showed that the weekly mortality
rate during the outbreak of the plague in Bombay
(1905–1906) is reasonably well described by the
function
eax
24. Consider the graph of y
. Use limits and
1+ eax
first derivatives to determine how the shape of this
curve depends on the parameter a.
25. In Example 6, we saw that the dose-response curve
f (t) = 890 sech²(0.2t
3.4) deaths/week
b
у —а +
а
1+ ex
where t is measured in weeks. Sketch this function
has asymptotes y = a and y = b, respectively, as x
approaches + o. Find the second derivative y" (x)
and discuss its properties including an equation that
can be used to identify any points of inflection, if
they exist.
26. In Example 4 of Section 2.7, we consider patterns of
local species richness of ants along an elevational
gradient. A function that best fits the data is
using information about asymptotes and first deriva-
tives. Recall that
sech x =
ex + e-*
31. In Example 4 we modeled the rate at which ac-
etaminophen diffuses from the stomach and in-
testines to the blood stream using this equation:
S =
= -10.3 + 24.9 x – 7.7x²
C(t) = 28.6(e¬0.31
e-) micrograms/milliliter
-
where x is elevation measured in kilometers and
Calculate the second derivative and discuss its
S is the number of species. Plot this function using
information about first derivatives.
behavior. Identify if the function C(t) has any points
of inflection for t > 0.
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