the string vibrates, (ii) when the tension is increased by turning a tuning peg, (iii) when the linear density is increased by switching to another string. 31. Suppose that the cost (in dollars) for a company to produce x pairs of a new line of jeans is C(x)= 2000 + 3x + 0.01x2 + 0.0002x' (a) Find the marginal cost function. (b) Find C'(100) and explain its meaning. What does it predict? (c) Compare C(100) with the cost of manufacturing the 101st pair of jeans. 32. The cost function for a certain commodity is 3. C(q) = 84 + 0.16q – 0.0006q?+ 0.000003q (a) Find and interpret C'(100). (b) Compare C'(100) with the cost of producing the 101st item. 33. If p(x) is the total value of the production when there are x workers in a plant, then the average productivity of the workforce at the plant is p(x) A(x) (a) Find A'(x). Why does the company want to hire more workers if A'(x) > 0? (b) Show that A'(x) > 0 if p'(x) is greater than the average productivity. 34. If R denotes the reaction of the body to some stimulus of strength x, the sensitivity S is defined to be the rate of change of the reaction with respect to x. A particular example is that when the brightness x of a light source is increased, the eye reacts by decreasing the area R of the pupil. The experimental formula 40 +24x04 0.4 1+4x has been used to model the dependence of R on x when R is measured in square millimeters and x is measured in appropriate units of brightness. (a) Find the sensitivity. (b) Illustrate part (a) by graphing both R and S as functions of x. Comment on the values of R and S at low levels of brightness. Is this what you would expect? 35. Patients undergo dialysis treatment to remove urea from their
the string vibrates, (ii) when the tension is increased by turning a tuning peg, (iii) when the linear density is increased by switching to another string. 31. Suppose that the cost (in dollars) for a company to produce x pairs of a new line of jeans is C(x)= 2000 + 3x + 0.01x2 + 0.0002x' (a) Find the marginal cost function. (b) Find C'(100) and explain its meaning. What does it predict? (c) Compare C(100) with the cost of manufacturing the 101st pair of jeans. 32. The cost function for a certain commodity is 3. C(q) = 84 + 0.16q – 0.0006q?+ 0.000003q (a) Find and interpret C'(100). (b) Compare C'(100) with the cost of producing the 101st item. 33. If p(x) is the total value of the production when there are x workers in a plant, then the average productivity of the workforce at the plant is p(x) A(x) (a) Find A'(x). Why does the company want to hire more workers if A'(x) > 0? (b) Show that A'(x) > 0 if p'(x) is greater than the average productivity. 34. If R denotes the reaction of the body to some stimulus of strength x, the sensitivity S is defined to be the rate of change of the reaction with respect to x. A particular example is that when the brightness x of a light source is increased, the eye reacts by decreasing the area R of the pupil. The experimental formula 40 +24x04 0.4 1+4x has been used to model the dependence of R on x when R is measured in square millimeters and x is measured in appropriate units of brightness. (a) Find the sensitivity. (b) Illustrate part (a) by graphing both R and S as functions of x. Comment on the values of R and S at low levels of brightness. Is this what you would expect? 35. Patients undergo dialysis treatment to remove urea from their
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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I need help with question #33 (both a & b) in page 236 of the James Stewart Calculus Eighth Edition textbook.
Transcribed Image Text:the string vibrates,
(ii) when the tension is increased by turning a tuning
peg,
(iii) when the linear density is increased by switching to
another string.
31. Suppose that the cost (in dollars) for a company to produce
x pairs of a new line of jeans is
C(x)= 2000 + 3x + 0.01x2 + 0.0002x'
(a) Find the marginal cost function.
(b) Find C'(100) and explain its meaning. What does it
predict?
(c) Compare C(100) with the cost of manufacturing the
101st pair of jeans.
32. The cost function for a certain commodity is
3.
C(q) = 84 + 0.16q – 0.0006q?+ 0.000003q
(a) Find and interpret C'(100).
(b) Compare C'(100) with the cost of producing the 101st
item.
33. If p(x) is the total value of the production when there are
x workers in a plant, then the average productivity of the
workforce at the plant is
p(x)
A(x)
(a) Find A'(x). Why does the company want to hire more
workers if A'(x) > 0?
(b) Show that A'(x) > 0 if p'(x) is greater than the average
productivity.
34. If R denotes the reaction of the body to some stimulus of
strength x, the sensitivity S is defined to be the rate of change
of the reaction with respect to x. A particular example is
that when the brightness x of a light source is increased,
the eye reacts by decreasing the area R of the pupil. The
experimental formula
40 +24x04
0.4
1+4x
has been used to model the dependence of R on x when
R is measured in square millimeters and x is measured in
appropriate units of brightness.
(a) Find the sensitivity.
(b) Illustrate part (a) by graphing both R and S as functions
of x. Comment on the values of R and S at low levels of
brightness. Is this what you would expect?
35. Patients undergo dialysis treatment to remove urea from their
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