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Mathematical Applications for the Management, Life, and Social SciencesSocial Security beneficiaries The table gives the number of millions of Social Security beneficiaries (actual and projected) for selected years from 1950 through 2030. Year Number of Beneficiaries (millions) Year Number of Beneficiaries (millions) 1950 2.9 2000 44.8 1960 14.3 2010 53.3 1970 25.2 2020 68.8 1980 35.1 2030 82.7 1990 39.5 Source: Social Security Trustees Report With B(t) representing the number of beneficiaries (in millions) t years past 1950, these data can be modeled by the function B ( t ) = ( 0.01 t + 3 ) ( 0.0238 t 2 − 9.79 t + 3100 ) − 9290 (a) Find the function that gives the instantaneous rate of change of the number of beneficiaries. (b) Find and interpret the instantaneous rate of change in 2020. (c) Use the data to determine which of the average rates of change (from 2010 to 2020, from 2020 to 2030, or from 2010 to 2030) best approximates the instantaneous rate from part (b).BuyFind*arrow_forward*

11th Edition

Ronald J. Harshbarger + 1 other

Publisher: Cengage Learning

ISBN: 9781305108042

Chapter 9.5, Problem 53E

Textbook Problem

** Social Security beneficiaries** The table gives the number of millions of Social Security beneficiaries (actual and projected) for selected years from 1950 through 2030.

Year |
Number of Beneficiaries (millions) |
Year |
Number of Beneficiaries (millions) |

1950 | 2.9 | 2000 | 44.8 |

1960 | 14.3 | 2010 | 53.3 |

1970 | 25.2 | 2020 | 68.8 |

1980 | 35.1 | 2030 | 82.7 |

1990 | 39.5 |

*Source:* Social Security Trustees Report

With *B(t)* representing the number of beneficiaries (in millions) *t* years past 1950, these data can be modeled by the function

(a) Find the function that gives the instantaneous rate of change of the number of beneficiaries.

(b) Find and interpret the instantaneous rate of change in 2020.

(c) Use the data to determine which of the average rates of change (from 2010 to 2020, from 2020 to 2030, or from 2010 to 2030) best approximates the instantaneous rate from part (b).

Mathematical Applications for the Management, Life, and Social Sciences

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Ch. 9.1 - 1. Can exist if is undefined?
Ch. 9.1 - 2. Does exist if ?
Ch. 9.1 - 3. Does
Ch. 9.1 - 4. If , does exist?
Ch. 9.1 - 5. Let
(a) Does
(b) Find .
Ch. 9.1 - 6. Evaluate the following limits (if they...Ch. 9.1 - In Problems 7-10, assume that f, g, and h are...Ch. 9.1 - In Problems 7-10, assume that f, g, and h are...Ch. 9.1 - In Problems 7-10, assume that f, g, and h are...Ch. 9.1 - In Problems 7-10, assume that f, g, and h are...

Ch. 9.1 - In Problems 1 -6, a graph of is shown and a...Ch. 9.1 - In Problems 1 -6, a graph of is shown and a...Ch. 9.1 - In Problems 1 -6, a graph of is shown and a...Ch. 9.1 - In Problems 1 -6, a graph of is shown and a...Ch. 9.1 - In Problems 1 -6, a graph of is shown and a...Ch. 9.1 - In Problems 1-6, a graph of y = f(x) is shown and...Ch. 9.1 - In Problems 7-10, use the graph of and the given...Ch. 9.1 - In Problems 7-10, use the graph of and the given...Ch. 9.1 - In Problems 7-10, use the graph of and the given...Ch. 9.1 - In Problems 7-10, use the graph of y = and the...Ch. 9.1 - In Problems 11-14, complete each table and predict...Ch. 9.1 - In Problems 11-14, complete each table and predict...Ch. 9.1 - In Problems 11-14, complete each table and predict...Ch. 9.1 - In Problems 11-14, complete each table and predict...Ch. 9.1 - In Problems 15-40, use properties of limits and...Ch. 9.1 - In Problems 15-40, use properties of limits and...Ch. 9.1 - In Problems 15-40, use properties of limits and...Ch. 9.1 - In Problems 15-40, use properties of limits and...Ch. 9.1 - In Problems 15-40, use properties of limits and...Ch. 9.1 - In Problems 15-40, use properties of limits and...Ch. 9.1 - In Problems 15-40, use properties of limits and...Ch. 9.1 - In Problems 15-40, use properties of limits and...Ch. 9.1 - In Problems 15-40, use properties of limits and...Ch. 9.1 - In Problems 15-40, use properties of limits and...Ch. 9.1 - In Problems 15-40, use properties of limits and...Ch. 9.1 - In Problems 15-40, use properties of limits and...Ch. 9.1 - In Problems 15-40, use properties of limits and...Ch. 9.1 - In Problems 15-40, use properties of limits and...Ch. 9.1 - In Problems 15-40, use properties of limits and...Ch. 9.1 - In Problems 15-40, use properties of limits and...Ch. 9.1 - In Problems 15-40, use properties of limits and...Ch. 9.1 - In Problems 15-40, use properties of limits and...Ch. 9.1 - In Problems 15-40, use properties of limits and...Ch. 9.1 - In Problems 15-40, use properties of limits and...Ch. 9.1 - In Problems 15-40, use properties of limits and...Ch. 9.1 - In Problems 15-40, use properties of limits and...Ch. 9.1 - In Problems 15-40, use properties of limits and...Ch. 9.1 - In Problems 15-40, use properties of limits and...Ch. 9.1 - In Problems 41-44, graph each function with a...Ch. 9.1 - In Problems 41-44, graph each function with a...Ch. 9.1 - In Problems 41-44, graph each function with a...Ch. 9.1 - In Problems 41-44, graph each function with a...Ch. 9.1 - In Problems 45-48, use the table feature of a...Ch. 9.1 - In Problems 45-48, use the table feature of a...Ch. 9.1 - In Problems 45-48, use the table feature of a...Ch. 9.1 - In Problems 45-48, use the table feature of a...Ch. 9.1 - 49. Use values 0.1, 0.01, 0.001, 0.0001, and...Ch. 9.1 - 50. (a) If if it exists. Explain your...Ch. 9.1 - 51. If and , find
(a)
(b)
(c)
(d)
Ch. 9.1 - 52. If and find
(a)
(b)
(c)
(d)
Ch. 9.1 - 53. If and , find
(a)
(b)
(c)
Ch. 9.1 - 54. If and , find
(a)
(b)
(c)
Ch. 9.1 - 55. Revenue The total revenue for a product is...Ch. 9.1 - 56. Profit If the profit function for a product is...Ch. 9.1 - 57. Sales and training The average monthly sales...Ch. 9.1 - 58. Sales and training During the first 4 months...Ch. 9.1 - 59. Advertising and sales Suppose that the daily...Ch. 9.1 - 60. Advertising and sales Sales y (in thousands of...Ch. 9.1 - 61. Productivity During an 8-hour shift, the rate...Ch. 9.1 - 62. Revenue If the revenue for a product is and...Ch. 9.1 - 63. Cost-benefit Suppose that the cost C of...Ch. 9.1 - 64. Cost-benefit Suppose that the cost C of...Ch. 9.1 - Federal income tax The following table shows part...Ch. 9.1 - 66. Parking costs The Ace Parking Garage charges...Ch. 9.1 - 67. Municipal water rates The Corner Water Corp....Ch. 9.1 - Airport parking Long-term parking at Savannah...Ch. 9.1 - Dow Jones Industrial Average The graph in the...Ch. 9.1 - Dow Jones Industrial Average The graph in the...Ch. 9.1 - Obesity Obesity (BMI ≥ 30) is a serious problem in...Ch. 9.1 - Obesity Obesity (BMI ≥ 30) is a serious problem in...Ch. 9.2 - 1. Find any x-values where the following functions...Ch. 9.2 - 2. If f(x) and g{x) arc polynomials,
is...Ch. 9.2 - 3. (a) Evaluate .
(b) What does part (a) say about...Ch. 9.2 - In Problems 1 and 2, refer to the figure. For each...Ch. 9.2 - In Problems 1 and 2, refer to the figure. For each...Ch. 9.2 - In Problems 3-8, determine whether each function...Ch. 9.2 - In Problems 3-8, determine whether each function...Ch. 9.2 - In Problems 3-8, determine whether each function...Ch. 9.2 - In Problems 3-8, determine whether each function...Ch. 9.2 - In Problems 3-8, determine whether each function...Ch. 9.2 - In Problems 3-8, determine whether each function...Ch. 9.2 - In Problems 9-16, determine whether the given...Ch. 9.2 - In Problems 9-16, determine whether the given...Ch. 9.2 - In Problems 9-16, determine whether the given...Ch. 9.2 - In Problems 9-16, determine whether the given...Ch. 9.2 - In Problems 9-16, determine whether the given...Ch. 9.2 - In Problems 9-16, determine whether the given...Ch. 9.2 - In Problems 9-16, determine whether the given...Ch. 9.2 - In Problems 9-16, determine whether the given...Ch. 9.2 - In Problems 17-20, use a graphing calculator to...Ch. 9.2 - In Problems 17-20, use a graphing calculator to...Ch. 9.2 - In Problems 17-20, use a graphing calculator to...Ch. 9.2 - In Problems 17-20, use a graphing calculator to...Ch. 9.2 -
Each of Problems 21-24 contains a function and...Ch. 9.2 - Each of Problems 21-24 contains a function and its...Ch. 9.2 - Each of Problems 21-24 contains a function and its...Ch. 9.2 - Each of Problems 21-24 contains a function and its...Ch. 9.2 - In Problems 25-32, complete (a) and (b).
(a) Use...Ch. 9.2 - In Problems 25-32, complete (a) and (b).
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(a) Use...Ch. 9.2 - In Problems 33 and 34, use a graphing calculator...Ch. 9.2 - In Problems 33 and 34, use a graphing calculator...Ch. 9.2 - In Problems 35 and 36, complete (a)-(c). Use...Ch. 9.2 - In Problems 35 and 36, complete (a)-(c). Use...Ch. 9.2 - For Problems 37 and 38, let
be a rational...Ch. 9.2 - For Problems 37 and 38, let
be a rational...Ch. 9.2 - 39. Sales volume Suppose that the weekly sales...Ch. 9.2 - 40. Worker productivity Suppose that the average...Ch. 9.2 - 41. Demand Suppose that the demand for a product...Ch. 9.2 - 42. Advertising and sales The sales volume y (in...Ch. 9.2 - 43. Annuities If an annuity can make an unending...Ch. 9.2 - 44. Response to adrenalin Experimental evidence...Ch. 9.2 - 45. Cost-benefit Suppose that the cost C of...Ch. 9.2 - 46. Pollution Suppose that the cost C of removing...Ch. 9.2 - 47. Pollution The percent p of particulate...Ch. 9.2 - 48. Cost-benefit The percent p of impurities that...Ch. 9.2 - Federal income tax The tax owed by a married...Ch. 9.2 - 50. Calories and temperature Suppose that the...Ch. 9.2 - Electrical usage costs The monthly charge in...Ch. 9.2 - Postage costs First-class postage for a standard...Ch. 9.2 - 52. U.S. smart phones Using data from 2010 to...Ch. 9.3 - 1. Find the average rate of change of over [1,...Ch. 9.3 - 2. For the function , find each of the...Ch. 9.3 - 3. Which of the following are given by ?
(a) The...Ch. 9.3 - 4. Must a graph that has no discontinuity, corner,...Ch. 9.3 - In Problems 1-4, for each given function, find the...Ch. 9.3 - In Problems 1-4, for each given function, find the...Ch. 9.3 - In Problems 1-4, for each given function, find the...Ch. 9.3 - In Problems 1-4, for each given function, find the...Ch. 9.3 - 5. Given , find the average rate of change of f(x)...Ch. 9.3 - 6. Given , find the average rate of change of f(x)...Ch. 9.3 - 7. In the Procedure/Example box in this section,...Ch. 9.3 - 8. In Example 6 in this section, we were given
....Ch. 9.3 - 9. Let .
(a) Use the definition of derivative and...Ch. 9.3 - 10. Let .
(a) Use the definition of derivative and...Ch. 9.3 - In Problems 11-14, the tangent line to the graph...Ch. 9.3 - In Problems 11-14, the tangent line to the graph...Ch. 9.3 - In Problems 11-14, the tangent line to the graph...Ch. 9.3 - In Problems 11-14, the tangent line to the graph...Ch. 9.3 - For each function in Problems 15-18, find
(a) the...Ch. 9.3 - For each function in Problems 15-18, find
(a) the...Ch. 9.3 - For each function in Problems 15-18, find
(a) the...Ch. 9.3 - For each function in Problems 15-18, find
(a) the...Ch. 9.3 - For each function in Problems 19-22, approximate...Ch. 9.3 - For each function in Problems 19-22, approximate...Ch. 9.3 - For each function in Problems 19-22, approximate...Ch. 9.3 - For each function in Problems 19-22, approximate...Ch. 9.3 - In Problems 23 and 24, use the given tables to...Ch. 9.3 - In Problems 23 and 24, use the given tables to...Ch. 9.3 - In the figures given in Problems 25 and 26, at...Ch. 9.3 - In the figures given in Problems 25 and 26, at...Ch. 9.3 - In Problems 27 and 28, a point on the graph of ...Ch. 9.3 - In Problems 27 and 28, a point on the graph of ...Ch. 9.3 - 29. If the instantaneous rate of change of f(x) at...Ch. 9.3 - 30. If the instantaneous rate of change of g(x) at...Ch. 9.3 - Because the derivative of a function represents...Ch. 9.3 - Because the derivative of a function represents...Ch. 9.3 - 33. Given the graph of ) in Figure 9.27, determine...Ch. 9.3 - 34. Given the graph of y = f(x) in Figure 9.27,...Ch. 9.3 - In Problems 35-38, (a) find the slope of the...Ch. 9.3 - In Problems 35-38, (a) find the slope of the...Ch. 9.3 - In Problems 35-38, (a) find the slope of the...Ch. 9.3 - In Problems 35-38, (a) find the slope of the...Ch. 9.3 - 39. Total cost Suppose total cost in dollars from...Ch. 9.3 - 40. Average velocity If an object is thrown upward...Ch. 9.3 - 41. Demand If the demand for a product is given...Ch. 9.3 - 42. Revenue If the total revenue function for a...Ch. 9.3 - 43. Total cost Suppose the figure shows the total...Ch. 9.3 - 44. b The figure shows the percent of the U.S....Ch. 9.3 - Marginal revenue The revenue function for a sound...Ch. 9.3 - 46. Marginal revenue Suppose the total revenue...Ch. 9.3 - 47. Labor force and output The monthly output at...Ch. 9.3 - 48. Consumer expenditure Suppose that the demand...Ch. 9.3 - 49. Profit Suppose that the profit function for...Ch. 9.3 - 50. Profit It the total revenue function and the...Ch. 9.3 - 51. Heat index The highest recorded temperature in...Ch. 9.3 - 52. Receptivity In learning theory, receptivity is...Ch. 9.3 - 53. Marginal revenue Suppose the graph shows a...Ch. 9.3 - 54. Social Security beneficiaries The graph shows...Ch. 9.4 - 1. True or false: The derivative of a constant...Ch. 9.4 - 2. True or false: The derivative of the sum of two...Ch. 9.4 - 3. True or false: The derivative of the difference...Ch. 9.4 - 4. Does the Coefficient Rule apply to , where c is...Ch. 9.4 - 5. Find the derivative of each of the following...Ch. 9.4 - 6. Find the slope of the line tangent to .
Ch. 9.4 - Find the derivatives of the functions in Problems...Ch. 9.4 - Find the derivatives of the functions in Problems...Ch. 9.4 - Find the derivatives of the functions in Problems...Ch. 9.4 - Find the derivatives of the functions in Problems...Ch. 9.4 - Find the derivatives of the functions in Problems...Ch. 9.4 - Find the derivatives of the functions in Problems...Ch. 9.4 - Find the derivatives of the functions in Problems...Ch. 9.4 - Find the derivatives of the functions in Problems...Ch. 9.4 - Find the derivatives of the functions in Problems...Ch. 9.4 - Find the derivatives of the functions in Problems...Ch. 9.4 - Find the derivatives of the functions in Problems...Ch. 9.4 - Find the derivatives of the functions in Problems...Ch. 9.4 - Find the derivatives of the functions in Problems...Ch. 9.4 - Find the derivatives of the functions in Problems...Ch. 9.4 - In Problems 15-18, at the indicated points,...Ch. 9.4 - In Problems 15-18, at the indicated points,...Ch. 9.4 - In Problems 15-18, at the indicated points,...Ch. 9.4 - In Problems 15-18, at the indicated points,...Ch. 9.4 - In Problems 19-26, find the derivative of each...Ch. 9.4 - In Problems 19-26, find the derivative of each...Ch. 9.4 - In Problems 19-26, find the derivative of each...Ch. 9.4 - In Problems 19-26, find the derivative of each...Ch. 9.4 - In Problems 19-26, find the derivative of each...Ch. 9.4 - In Problems 19-26, find the derivative of each...Ch. 9.4 - In Problems 19-26, find the derivative of each...Ch. 9.4 - In Problems 19-26, find the derivative of each...Ch. 9.4 - In Problems 27-30, write the equation of the...Ch. 9.4 - In Problems 27-30, write the equation of the...Ch. 9.4 - In Problems 27-30, write the equation of the...Ch. 9.4 - In Problems 27-30, write the equation of the...Ch. 9.4 - In Problems 31-34, find the coordinates of points...Ch. 9.4 - In Problems 31-34, find the coordinates of points...Ch. 9.4 - In Problems 31-34, find the coordinates of points...Ch. 9.4 - In Problems 31-34, find the coordinates of points...Ch. 9.4 - In Problems 35 and 36, find each derivative at...Ch. 9.4 - In Problems 35 and 36, find each derivative at...Ch. 9.4 - In Problems 37-40, complete the following. (a)...Ch. 9.4 - In Problems 37-40, complete the following. (a)...Ch. 9.4 - In Problems 37-40, complete the following. (a)...Ch. 9.4 - In Problems 37-40, complete the following. (a)...Ch. 9.4 - The tangent line to a curve at a point closely...Ch. 9.4 - The tangent line to a curve at a point closely...Ch. 9.4 - For each function in Problems 43-46, do the...Ch. 9.4 - For each function in Problems 43-46, do the...Ch. 9.4 - For each function in Problems 43-46, do the...Ch. 9.4 - For each function in Problems 43-46, do the...Ch. 9.4 - 47. Revenue Suppose that a wholesaler expects that...Ch. 9.4 - 48. Revenue The total revenue, in dollars, for a...Ch. 9.4 - 49. Metabolic rate According to Kleiber's law, the...Ch. 9.4 - 50. Capital investment and output The monthly...Ch. 9.4 - 51. Demand The demand for q units of a product...Ch. 9.4 - 52. Demand Suppose that the demand tor a product...Ch. 9.4 - 53. Cost and average cost Suppose that the total...Ch. 9.4 - 54. Cost and average cost Suppose that the total...Ch. 9.4 - 55. Cost-benefit Suppose that tor a certain city,...Ch. 9.4 - 56. Cost-benefit Suppose that the cost C, in...Ch. 9.4 - 57. Wind chill One form of the formula that...Ch. 9.4 - 58. Allometric relationships—crabs Data for...Ch. 9.5 - 1. True or false: The derivative of the product of...Ch. 9.5 - 2. True or false: The derivative of the quotient...Ch. 9.5 - 3. Find for each of the following.
(a) Do not...Ch. 9.5 - 4. If , does finding y' require the Product Rule?...Ch. 9.5 - 5. If , where c is a constant, does finding y'...Ch. 9.5 - In Problems 1-4, find the derivative and...Ch. 9.5 - In Problems 1-4, find the derivative and...Ch. 9.5 - In Problems 1-4, find the derivative and...Ch. 9.5 - In Problems 1-4, find the derivative and...Ch. 9.5 - In Problems 5-8, find the derivative but do not...Ch. 9.5 - In Problems 5-8, find the derivative but do not...Ch. 9.5 - In Problems 5-8, find the derivative but do not...Ch. 9.5 - In Problems 5-8, find the derivative but do not...Ch. 9.5 - In Problems 9 and 10, at each indicated point,...Ch. 9.5 - In Problems 9 and 10, at each indicated point,...Ch. 9.5 - In Problems 11-20, find the indicated derivatives...Ch. 9.5 - In Problems 11-20, find the indicated derivatives...Ch. 9.5 - In Problems 11-20, find the indicated derivatives...Ch. 9.5 - In Problems 11-20, find the indicated derivatives...Ch. 9.5 - In Problems 11-20, find the indicated derivatives...Ch. 9.5 - In Problems 11-20, find the indicated derivatives...Ch. 9.5 - In Problems 11-20, find the indicated derivatives...Ch. 9.5 - In Problems 11-20, find the indicated derivatives...Ch. 9.5 - In Problems 11-20, find the indicated derivatives...Ch. 9.5 - In Problems 11-20, find the indicated derivatives...Ch. 9.5 - In Problems 21 and 22, at the indicated point for...Ch. 9.5 - In Problems 21 and 22, at the indicated point for...Ch. 9.5 - In Problems 23-26, write the equation of the...Ch. 9.5 - In Problems 23-26, write the equation of the...Ch. 9.5 - In Problems 23-26, write the equation of the...Ch. 9.5 - In Problems 23-26, write the equation of the...Ch. 9.5 - In Problems 27-30, use the numerical derivative...Ch. 9.5 - In Problems 27-30, use the numerical derivative...Ch. 9.5 - In Problems 27-30, use the numerical derivative...Ch. 9.5 - In Problems 27-30, use the numerical derivative...Ch. 9.5 - In Problems 35 and 36,
(a) find f'(x).
(b) graph...Ch. 9.5 - In Problems 35 and 36,
(a) find f'(x).
(b) graph...Ch. 9.5 - 37. Prove the Quotient Rule for differentiation....Ch. 9.5 - 38. Use the Quotient Rule to show that the Powers...Ch. 9.5 - 39. Cost-bene fit If the cost C (in dollars) of...Ch. 9.5 - 40. Cost-benefit If the cost C (in dollars) of...Ch. 9.5 - 41. Revenue Suppose the revenue (in dollars) from...Ch. 9.5 - 42. Revenue The revenue (in dollars) from the sale...Ch. 9.5 - 43. Revenue A travel agency will plan a group tour...Ch. 9.5 - 44. Revenue McRobert's Electronics sells 200 TVs...Ch. 9.5 - 45. Response to a drug The reaction R to an...Ch. 9.5 - 46. Nerve response The number of action potentials...Ch. 9.5 - 47. Test reliability If a test having reliability...Ch. 9.5 - 48. Advertising and sales The sales of a product s...Ch. 9.5 - 49. Candidate recognition Suppose that the...Ch. 9.5 - 50. Endangered species population It is determined...Ch. 9.5 - 51. Wind chill Each winter the so-called “polar...Ch. 9.5 - 52. Response to injected adrenalin Experimental...Ch. 9.5 - 53. Social Security beneficiaries The table gives...Ch. 9.5 - 54. Emissions The table shows data for sulfur...Ch. 9.5 - 55. Females in the workforce For selected years...Ch. 9.5 - 56. Alzheimer's As the baby boomer generation ages...Ch. 9.6 -
Ch. 9.6 - 2. (a) If , find f'(x) by using the Power Rule...Ch. 9.6 - IN Problems 1-4, find dydu,dudx,anddydx....Ch. 9.6 - In Problems 1-4, find dydu,dudx,anddydx....Ch. 9.6 - In Problems 1-4, find dydu,dudx,anddydx....Ch. 9.6 - In Problems 1-4, find dydu,dudx,anddydx....Ch. 9.6 - Differentiate the functions in Problems 3-20.
3.
Ch. 9.6 - Differentiate the functions in Problems 3-20.
4.
Ch. 9.6 - Differentiate the functions in Problems 3-20.
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Ch. 9.6 - Differentiate the functions in Problems 3-20.
6.
Ch. 9.6 - Differentiate the functions in Problems 3-20.
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Ch. 9.6 - Differentiate the functions in Problems 3-20.
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Ch. 9.6 - Differentiate the functions in Problems 3-20.
9.
Ch. 9.6 - Differentiate the functions in Problems 3-20.
10....Ch. 9.6 - Differentiate the functions in Problems 3-20.
11....Ch. 9.6 - Differentiate the functions in Problems 3-20.
12....Ch. 9.6 - Differentiate the functions in Problems 3-20.
13....Ch. 9.6 - Differentiate the functions in Problems 3-20.
14....Ch. 9.6 - Differentiate the functions in Problems 3-20.
15....Ch. 9.6 - Differentiate the functions in Problems 3-20.
16....Ch. 9.6 - Differentiate the functions in Problems 3-20.
17....Ch. 9.6 - Differentiate the functions in Problems 3-20.
18....Ch. 9.6 - Differentiate the functions in Problems 3-20.
19....Ch. 9.6 - Differentiate the functions in Problems 3-20.
20....Ch. 9.6 - At the indicated point, for each function in...Ch. 9.6 - At the indicated point, for each function in...Ch. 9.6 - At the indicated point, for each function in...Ch. 9.6 - At the indicated point, for each function in...Ch. 9.6 - In Problems 25-28, write the equation of the line...Ch. 9.6 - In Problems 25-28, write the equation of the line...Ch. 9.6 - In Problems 25-28, write the equation of the line...Ch. 9.6 - In Problems 25-28, write the equation of the line...Ch. 9.6 - In Problems 29 and 30, complete the following for...Ch. 9.6 - In Problems 29 and 30, complete the following for...Ch. 9.6 - In Problems 31 and 32, do the following for each...Ch. 9.6 - In Problems 31 and 32, do the following for each...Ch. 9.6 - In Problems 33 and 34, find the derivative of each...Ch. 9.6 - In Problems 33 and 34, find the derivative of each...Ch. 9.6 - 35. Ballistics Ballistics experts are able to...Ch. 9.6 - 36. Population of microorganisms Suppose that the...Ch. 9.6 - 37. Revenue The revenue from the sale of a product...Ch. 9.6 - 38. Revenue The revenue from the sale of x units...Ch. 9.6 - 39. Pricing and sales Suppose that the weekly...Ch. 9.6 - 40. Pricing and sales A chain of auto service...Ch. 9.6 - 41. Demand Suppose that the demand tor q units of...Ch. 9.6 - Stimulus-response The relation between the...Ch. 9.6 - Stimulus-response The relation between the...Ch. 9.6 - Stimulus-response The relation between the...Ch. 9.6 - 45. Demand If the demand for q units of a product...Ch. 9.6 - 46. Advertising and sales The daily sales S (in...Ch. 9.6 - 47. Body-heat loss The description of body-heat...Ch. 9.6 - 48. Data entry speed The data entry speed (in...Ch. 9.6 - 49. Investments If an IRA is a variable-rate...Ch. 9.6 - 50. Concentration of body substances The...Ch. 9.6 - National health expenditures The table shows the...Ch. 9.6 - 52. Energy use Energy use per dollar of GDP...Ch. 9.6 - Gross domestic product The table shows U.S. gross...Ch. 9.6 - 54. Diabetes The figure shows the percent of the...Ch. 9.7 - 1. If a function has the form , where n is a...Ch. 9.7 - 2. If a function has the form ”, where n is a...Ch. 9.7 - 3. Find the derivative of each of the following...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - Find the derivatives of the functions in Problems...Ch. 9.7 - In Problems 33 and 34, find the derivative of each...Ch. 9.7 - In Problems 33 and 34, find the derivative of each...Ch. 9.7 - 35. Physical output The total physical output P of...Ch. 9.7 - 36. Revenue Suppose that the revenue function for...Ch. 9.7 - 37. Revenue Suppose that the revenue in dollars...Ch. 9.7 - 38. Production Suppose that the production of x...Ch. 9.7 - 39. National consumption If the national...Ch. 9.7 - 40. Demand Suppose that the demand function for q...Ch. 9.7 - 41. Volume When squares of side x inches are cut...Ch. 9.7 - 42. Advertising and sales Suppose that sales (in...Ch. 9.7 - 43. Advertising and sales An inferior product with...Ch. 9.7 - 44. Advertising and sales An excellent film with a...Ch. 9.7 - Per capita expenditures for U.S. health care The...Ch. 9.8 - Suppose that the distance a particle travels is...Ch. 9.8 - Suppose that the distance a particle travels is...Ch. 9.8 - Suppose that the distance a particle travels is...Ch. 9.8 - Suppose that the distance a particle travels is...Ch. 9.8 - In Problems 1-6, find the second derivative.
Ch. 9.8 - In Problems 1-6, find the second derivative.
Ch. 9.8 - In Problems 1-6, find the second derivative.
Ch. 9.8 - In Problems 1-6, find the second derivative.
Ch. 9.8 - In Problems 1-6, find the second derivative.
Ch. 9.8 - In Problems 1-6, find the second derivative.
Ch. 9.8 - In Problems 7-12, find the third derivative.
Ch. 9.8 - In Problems 7-12, find the third derivative.
Ch. 9.8 - In Problems 7-12, find the third derivative.
Ch. 9.8 - In Problems 7-12, find the third derivative.
Ch. 9.8 - In Problems 7-12, find the third derivative.
Ch. 9.8 - In Problems 7-12, find the third derivative.
Ch. 9.8 - In Problems 13-24, find the indicated...Ch. 9.8 - In Problems 13-24, find the indicated...Ch. 9.8 - In Problems 13-24, find the indicated...Ch. 9.8 - In Problems 13-24, find the indicated...Ch. 9.8 - In Problems 13-24, find the indicated...Ch. 9.8 - In Problems 13-24, find the indicated...Ch. 9.8 - In Problems 13-24, find the indicated...Ch. 9.8 - In Problems 13-24, find the indicated...Ch. 9.8 - In Problems 13-24, find the indicated...Ch. 9.8 - In Problems 13-24, find the indicated...Ch. 9.8 - In Problems 13-24, find the indicated...Ch. 9.8 - In Problems 13-24, find the indicated...Ch. 9.8 - 25. If , what is the rate of change of at (1,...Ch. 9.8 - 26. If , what is the rate of change of y' at (1,...Ch. 9.8 - In Problems 27-30, use the numerical derivative...Ch. 9.8 - In Problems 27-30, use the numerical derivative...Ch. 9.8 - In Problems 27-30, use the numerical derivative...Ch. 9.8 - In Problems 27-30, use the numerical derivative...Ch. 9.8 -
31.
Ch. 9.8 -
32.
Ch. 9.8 - 33. Acceleration A particle travels as a function...Ch. 9.8 - 34. Acceleration If the formula describing the...Ch. 9.8 - 35. Revenue The revenue (in dollars) from the sale...Ch. 9.8 - 36. Revenue Suppose that the revenue (in dollars)...Ch. 9.8 - 37. Sensitivity When medicine is administered,...Ch. 9.8 - 38. Photosynthesis The amount of photosynthesis...Ch. 9.8 - 39. Revenue The revenue (in thousands of dollars)...Ch. 9.8 - 40. Advertising and sales The sales of a product S...Ch. 9.8 - 41. Advertising and sales The daily sales S (in...Ch. 9.8 - 42. Advertising and sales A product with a large...Ch. 9.8 - 43. Average annual wage Using Social Security...Ch. 9.8 - 44. Demographics The makeup of various groups...Ch. 9.8 - 47. Income by age The median income, in thousands...Ch. 9.9 - Suppose the total cost function for a commodity is...Ch. 9.9 - Suppose the total cost function for a commodity is...Ch. 9.9 - Suppose the total cost function for a commodity is...Ch. 9.9 - Suppose the total cost function for a commodity is...Ch. 9.9 - Suppose the total cost function for a commodity is...Ch. 9.9 - If the total profit function for a product is ,...Ch. 9.9 - If the total profit function for a product is ,...Ch. 9.9 - In Problems 1-8, total revenue is in dollars and x...Ch. 9.9 - In Problems 1-8, total revenue is in dollars and x...Ch. 9.9 - MARGINAL REVENUE, COST, AND PROFIT In Problems...Ch. 9.9 - MARGINAL REVENUE, COST, AND PROFIT In Problems...Ch. 9.9 - MARGINAL REVENUE, COST, AND PROFIT In Problems...Ch. 9.9 - In Problems 1-8, total revenue is in dollars and x...Ch. 9.9 - MARGINAL REVENUE, COST, AND PROFIT In Problems...Ch. 9.9 - MARGINAL REVENUE, COST, AND PROFIT In Problems...Ch. 9.9 - In Problems 9-16, cost is in dollars and x is the...Ch. 9.9 - In Problems 9-16, cost is in dollars and x is the...Ch. 9.9 - In Problems 9-16, cost is in dollars and x is the...Ch. 9.9 - In Problems 9-16, cost is in dollars and x is the...Ch. 9.9 - In Problems 9-16, cost is in dollars and x is the...Ch. 9.9 - In Problems 9-16, cost is in dollars and x is the...Ch. 9.9 - In Problems 9-16, cost is in dollars and x is the...Ch. 9.9 - In Problems 9-16, cost is in dollars and x is the...Ch. 9.9 - 17. Suppose that the cost function for a commodity...Ch. 9.9 - Suppose that the cost function for a commodity is...Ch. 9.9 - 19. If the cost function for a commodity is
...Ch. 9.9 - 20. If the cost function for a commodity is
...Ch. 9.9 - 21. If the cost function for a commodity is
graph...Ch. 9.9 - 22. If the cost function for a commodity is
graph...Ch. 9.9 - In each of Problems 23 and 24, the graph of a...Ch. 9.9 - In each of Problems 23 and 24, the graph of a...Ch. 9.9 - In Problems 25-28, cost, revenue, and profit are...Ch. 9.9 - In Problems 25-28, cost, revenue, and profit are...Ch. 9.9 - In Problems 25-28, cost, revenue, and profit are...Ch. 9.9 - In Problems 25-28, cost, revenue, and profit are...Ch. 9.9 - In each of Problems 29 and 30, the graphs of a...Ch. 9.9 - In each of Problems 29 and 30, the graphs of a...Ch. 9.9 - In each of Problems 31 and 32, the graph of a...Ch. 9.9 - In each of Problems 31 and 32, the graph of a...Ch. 9.9 - 33. (a) Graph the marginal profit function for the...Ch. 9.9 - 34. (a) Graph the marginal profit function for the...Ch. 9.9 - 35. The price of a product in a competitive market...Ch. 9.9 - 36. The cost per unit of producing a product is ...Ch. 9.9 - 37. If the daily cost per unit of producing a...Ch. 9.9 - 38. The Mary Ellen Candy Company produces...Ch. 9 - In Problems 1-6, use the graph of in Figure 9.40...Ch. 9 - In Problems 1-6, use the graph of in Figure 9.40...Ch. 9 - In Problems 1-6, use the graph of y=f(x) in Figure...Ch. 9 - In Problems 1-6, use the graph of in Figure 9.40...Ch. 9 - In Problems 1-6, use the graph of in Figure 9.40...Ch. 9 - In Problems 1-6, use the graph of in Figure 9.40...Ch. 9 - In Problems 7-20, find each limit, if it exists.
Ch. 9 - In Problems 7-20, find each limit, if it exists.
Ch. 9 - In Problems 7-20, find each limit, if it exists.
Ch. 9 - In Problems 7-20, find each limit, if it exists.
Ch. 9 - In Problems 7-20, find each limit, if it exists.
Ch. 9 - In Problems 7-20, find each limit, if it exists.
Ch. 9 - In Problems 7-20, find each limit, if it exists.
Ch. 9 - In Problems 7-20, find each limit, if it exists.
Ch. 9 - In Problems 7-20, find each limit, if it exists.
Ch. 9 - In Problems 7-20, find each limit, if it exists.
Ch. 9 - ssIn Problems 7-20, find each limit, if it...Ch. 9 - In Problems 7-20, find each limit, if it exists.
Ch. 9 - In Problems 7-20, find each limit, if it...Ch. 9 - In Problems 7-20, find each limit, if it...Ch. 9 - In Problems 21 and 22, use tables to investigate...Ch. 9 - In Problems 21 and 22, use tables to investigate...Ch. 9 - Use the graph of y = f(x) in Figure 9.40 to answer...Ch. 9 - Use the graph of y = f(x) in Figure 9.40 to answer...Ch. 9 - In Problems 25-30, suppose that
25. What is ?
Ch. 9 - In Problems 25-30, suppose that
26. What is if...Ch. 9 - In Problems 25-30, suppose that
27. What is if...Ch. 9 - In Problems 25-30, suppose that
29. Is ...Ch. 9 - In Problems 25-30, suppose that
29. Is ...Ch. 9 - In Problems 25-30, suppose that
30. Is ...Ch. 9 - For the functions in Problems 31-34, determine...Ch. 9 - For the functions in Problems 31-34, determine...Ch. 9 - For the functions in Problems 31-34, determine...Ch. 9 - For the functions in Problems 31-34, determine...Ch. 9 - In Problems 35 and 36, use the graphs to find (a)...Ch. 9 - In Problems 35 and 36, use the graphs to find (a)...Ch. 9 - In Problems 37 and 38, evaluate the limits, if...Ch. 9 - In Problems 37 and 38, evaluate the limits, if...Ch. 9 - 39. Find the average rate of change of
Ch. 9 - In Problems 40 and 41, decide whether the...Ch. 9 - In Problems 40 and 41, decide whether the...Ch. 9 - 42. Use the definition of derivative to find .
Ch. 9 - 43. Use the definition of derivative to find .
Ch. 9 - Use the graph of y = f(x) in Figure 9.40 on the...Ch. 9 - Use the graph of y = f(x) in Figure 9.40 on the...Ch. 9 - Use the graph of y = f(x) in Figure 9.40 on the...Ch. 9 - 47. Let . Approximate f'(2)
(a) by using the...Ch. 9 - 48. Use the given table of values for g(x) to
(a)...Ch. 9 - Use the following graph of f(x) to complete...Ch. 9 - Use the following graph of f(x) to complete...Ch. 9 - 51. If
Ch. 9 - 52. If
Ch. 9 - 53. If
Ch. 9 - 54. If
Ch. 9 - 55. If
Ch. 9 - 56. If
Ch. 9 - 57. If find y’.
Ch. 9 - 58. If ,find .
Ch. 9 - 59. Write the equation of the line tangent to the...Ch. 9 - 60. Write the equation of the line tangent to the...Ch. 9 - In Problems 61 and 62, (a) find all x-values...Ch. 9 - In Problems 61 and 62, (a) find all x-values...Ch. 9 - 63. If
Ch. 9 -
Ch. 9 -
Ch. 9 -
Ch. 9 -
Ch. 9 -
Ch. 9 -
Ch. 9 -
Ch. 9 -
Ch. 9 - .
Ch. 9 -
Ch. 9 - 74. Find S' if S =
Ch. 9 -
Ch. 9 -
Ch. 9 -
Ch. 9 -
Ch. 9 - In Problems 79 and 80, find the second...Ch. 9 - In Problems 79 and 80, find the second...Ch. 9 - In Problems 81 and 82, find the fifth...Ch. 9 - In Problems 81 and 82, find the fifth...Ch. 9 - 83. If .
Ch. 9 - 84. If , find .
Ch. 9 - Cost, revenue, and profit In Problems 85-88,...Ch. 9 - Cost, revenue, and profit In Problems 85-88,...Ch. 9 - Cost, revenue, and profit In Problems 85-88,...Ch. 9 - Cost, revenue, and profit In Problems 85-88,...Ch. 9 - Elderly in the workforce The graph shows the...Ch. 9 - Elderly in the workforce The graph shows the...Ch. 9 - 91. Demand Suppose that the demand for x units of...Ch. 9 - 92. Severe weather ice makers Thunderstorms severe...Ch. 9 - 93. Revenue The graph shows the revenue function...Ch. 9 - 94. Revenue In a 100-unit apartment building when...Ch. 9 - 95. Productivity Suppose the productivity of a...Ch. 9 - 96. Demand The demand q for a product at price p...Ch. 9 - 97. Supply The number of units x of a product that...Ch. 9 - 98. Acceleration Suppose an object moves so that...Ch. 9 - 99. Profit Suppose a company’s profit (in dollars)...Ch. 9 - In Problems 100-107, cost, revenue, and profit are...Ch. 9 - In Problems 100-107, cost, revenue, and profit are...Ch. 9 -
In Problems 100-107, cost, revenue, and profit...Ch. 9 - In Problems 100-107, cost, revenue, and profit are...Ch. 9 - In Problems 100-107, cost, revenue, and profit are...Ch. 9 - In Problems 100-107, cost, revenue, and profit are...Ch. 9 - In Problems 100-107, cost, revenue, and profit are...Ch. 9 - In Problems 100-107, cost, revenue, and profit are...Ch. 9 - 108. Cost, revenue, and profit The graph shows the...Ch. 9 - Evaluate the following limits, if they exist. Use...Ch. 9 - 5. (a) Write the limit definition for .
(b) Use...Ch. 9 - 6. Let Identify all x-values where is not...Ch. 9 - Use derivative formulas to find the derivative of...Ch. 9 - 14. Find .
Ch. 9 - 15. Let .
(a) Write the equation of the line...Ch. 9 - 16. Find the average rate of change of over...Ch. 9 - 18. Use the definition of continuity to...Ch. 9 - In Problems 19 and 20, suppose a company has its...Ch. 9 - In Problems 19 and 20, suppose a company has its...Ch. 9 - 21. Suppose that is a differentiable function. Use...Ch. 9 - 22. Use the graph to perform the evaluations...Ch. 9 - 23. Given that the line is tangent to the...

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