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
#51, 52, 54
![50. Car tires to be c
table tire life L (in of for a certain
(a) Use a or to life
underinflation can cause The data in t
(b) Calculate dV/
of the derivative? What are its
the curve at the
nd the tangent line
the
V, (1, 0)
underinflation can cause premature treadware. The daion
fand use them
type of tire at various pressures P (in lb/in?).
42
35
45
31
74
99
aph the func-
the viewing
with a quadratic function of the pressure.
(b) Use the model to estimate dL/dP when P
a.
make
See
graphing
in part (b).
the units? What is the significance of the signs of the
derivatives?
51. Find the points on the curve y = 2x' + 3x² – 12x + 1
where the tangent is horizontal.
the func-
-1, 4]
52. For what value of x does the graph of f(x) = e* – 2x have a
horizontal tangent?
3
53. Show that the curve y = 2e* + 3x + 5x° has no tangent line
with slope 2.
(s) 2K
hing
art (b).
54. Find an equation of the tangent line to the curve y = x/x
that is parallel to the line y = 1 + 3x.
55. Find equations of both lines that are tangent to the curve
y 1 +x' and parallel to the line 12x - y = 1.
3
56. At what point on the curve y = 1 + 2e* - 3x is the tangent
line parallel to the line 3x – y = 5? Illustrate by graphing
the curve and both lines.
ne
%3D
57. Find an equation of the normal line to the parabola
y = x² - 5x + 4 that is parallel to the line x- 3y = 5.
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96529d31-1af4-4d90-b6c1-79b0ae971a1c%2F5dd64ca5-caea-4c1c-b088-481c8df08cb9%2F0uxylv.jpeg&w=3840&q=75)
Transcribed Image Text:50. Car tires to be c
table tire life L (in of for a certain
(a) Use a or to life
underinflation can cause The data in t
(b) Calculate dV/
of the derivative? What are its
the curve at the
nd the tangent line
the
V, (1, 0)
underinflation can cause premature treadware. The daion
fand use them
type of tire at various pressures P (in lb/in?).
42
35
45
31
74
99
aph the func-
the viewing
with a quadratic function of the pressure.
(b) Use the model to estimate dL/dP when P
a.
make
See
graphing
in part (b).
the units? What is the significance of the signs of the
derivatives?
51. Find the points on the curve y = 2x' + 3x² – 12x + 1
where the tangent is horizontal.
the func-
-1, 4]
52. For what value of x does the graph of f(x) = e* – 2x have a
horizontal tangent?
3
53. Show that the curve y = 2e* + 3x + 5x° has no tangent line
with slope 2.
(s) 2K
hing
art (b).
54. Find an equation of the tangent line to the curve y = x/x
that is parallel to the line y = 1 + 3x.
55. Find equations of both lines that are tangent to the curve
y 1 +x' and parallel to the line 12x - y = 1.
3
56. At what point on the curve y = 1 + 2e* - 3x is the tangent
line parallel to the line 3x – y = 5? Illustrate by graphing
the curve and both lines.
ne
%3D
57. Find an equation of the normal line to the parabola
y = x² - 5x + 4 that is parallel to the line x- 3y = 5.
%3D
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