Question 1

Suppose that air is being pumped into a spherical balloon at a rate of 12 in3/min.At what rate is the radius of the balloon increasing when the radius is 9 in?

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 2

Between the years 1960 and 2002, the percent of women in the work force can be modeled by   , where x is the number of years past 1950 (Source: U.S. Bureau of Labor Statistics). If this model is accurate beyond 2002, at what rate will the percent be changing in 2013? ​

Accepted Answer

A)  In 2013, the rate will be changing at 0.291% per year. 
B)  In 2013, the rate will be changing at 0.455% per year. 
C)  In 2013, the rate will be changing at 0.007% per year. 
D)  In 2013, the rate will be changing at 1.324% per year. 
E)  In 2013, the rate will be changing at 0.231% per year. 
A)  In 2013, the rate will be changing at 0.291% per year. 
B)  In 2013, the rate will be changing at 0.455% per year. 
C)  In 2013, the rate will be changing at 0.007% per year. 
D)  In 2013, the rate will be changing at 1.324% per year. 
E)  In 2013, the rate will be changing at 0.231% per year.

Question 3

Find   . ​
​   ​

Accepted Answer

A)    
B)    
C)  ​   
D)    
E)    
A)    
B)    
C)  ​   
D)    
E)

Question 4

For the given equation, find the slope of the tangent to the curve at the point   . Round your answer to two decimal places. ​   ​

Accepted Answer

A)  -0.94 
B)  -1.06 
C)  -0.27 
D)  0.00 
E)  undefined 
A)  -0.94 
B)  -1.06 
C)  -0.27 
D)  0.00 
E)  undefined

Question 5

Assume that x and y are differentiable functions of t. In each case, find   given that   ,   , and   . ​   ​

Accepted Answer

A)  11 
B)  13 
C)  22 
D)  1 
E)  -22 
A)  11 
B)  13 
C)  22 
D)  1 
E)  -22

Question 6

Find the derivative of the following function. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 7

Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the radius of the tumor to decrease at a rate of 9 millimeters per month. At what rate is the surface area of the tumor decreasing when the radius is 2 mm? ​

Accepted Answer

A)  Surface area is decreasing at the rate of 288π mm2/month. 
B)  Surface area is decreasing at the rate of 72π mm2/month. 
C)  Surface area is decreasing at the rate of 32π mm2/month. 
D)  Surface area is decreasing at the rate of 16π mm2/month. 
E)  Surface area is decreasing at the rate of 144π mm2/month. 
A)  Surface area is decreasing at the rate of 288π mm2/month. 
B)  Surface area is decreasing at the rate of 72π mm2/month. 
C)  Surface area is decreasing at the rate of 32π mm2/month. 
D)  Surface area is decreasing at the rate of 16π mm2/month. 
E)  Surface area is decreasing at the rate of 144π mm2/month.

Question 8

Find the y-value at the relative minima, and use a graphing utility to check your result. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  does not exist 
A)    
B)    
C)    
D)    
E)  does not exist

Question 9

Suppose that a boat is being pulled toward a dock by a winch that is 24 ft above the level of the boat deck. If the winch is pulling the cable at a rate of 26 ft/min, at what rate is the boat approaching the dock when it is 32 ft from the dock? Use the figure below. Round your answer to two decimal places. ​   ​

Accepted Answer

A)  32.50 ft/min 
B)  26.00 ft/min 
C)  43.33 ft/min 
D)  20.80 ft/min 
E)  15.60 ft/min 
A)  32.50 ft/min 
B)  26.00 ft/min 
C)  43.33 ft/min 
D)  20.80 ft/min 
E)  15.60 ft/min

Question 10

Suppose a 170-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 1 ft/sec, at what rate is the top of the ladder sliding down the wall when the bottom is 26 ft from the wall? ​

Accepted Answer

A)  The top of the ladder is sliding down the wall at the rate of   ft/sec. 
B)  The top of the ladder is sliding down the wall at the rate of   ft/sec. 
C)  The top of the ladder is sliding down the wall at the rate of   ft/sec. 
D)  The top of the ladder is sliding down the wall at the rate of   ft/sec. 
E)  The top of the ladder is sliding down the wall at the rate of   ft/sec. 
A)  The top of the ladder is sliding down the wall at the rate of   ft/sec. 
B)  The top of the ladder is sliding down the wall at the rate of   ft/sec. 
C)  The top of the ladder is sliding down the wall at the rate of   ft/sec. 
D)  The top of the ladder is sliding down the wall at the rate of   ft/sec. 
E)  The top of the ladder is sliding down the wall at the rate of   ft/sec.

Question 11

Find   if   . ​

Accepted Answer

A)    
B)    
C)  ​   
D)    
E)    
A)    
B)    
C)  ​   
D)    
E)

Question 12

If   find y'.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 13

Suppose that a company's sales volume y (in dollars) is related to its advertising expenditures x (in dollars) according to   Find the rate of change of sales volume, with respect to advertising expenditures when x = $70. Round your answer to two decimal places.

Accepted Answer

A)  2.96 
B)  0.84 
C)  0.66 
D)  0.19 
E)  0.24 
A)  2.96 
B)  0.84 
C)  0.66 
D)  0.19 
E)  0.24

Question 14

Suppose that the revenue in dollars from the sale of x units of a product is given by   . Find the marginal revenue function. ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

For many species of fish, the allometric relationship between the weight W and the length L is approximately   where k is a constant. For   find the percent rate of change of the weight as a corresponding percent rate of change of the length. ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

The radius of a circle is increasing at a rate of 6 ft/min. At what rate is its area changing when the radius is 7 ft? ​

Accepted Answer

A)    sq ft/min 
B)    sq ft/min 
C)    sq ft/min 
D)    sq ft/min 
E)    sq ft/min 
A)    sq ft/min 
B)    sq ft/min 
C)    sq ft/min 
D)    sq ft/min 
E)    sq ft/min

Question 17

The supply function for a product is given by   , where x is the number of units supplied and p is the price in dollars. If the price is increasing at a rate of $1 per month, at what rate is the supply changing when   Round your answer to three decimal places. ​

Accepted Answer

A)  0.013 units per month 
B)  0.299 units per month 
C)  0.043 units per month 
D)  0.066 units per month 
E)  0.033 units per month 
A)  0.013 units per month 
B)  0.299 units per month 
C)  0.043 units per month 
D)  0.066 units per month 
E)  0.033 units per month

Question 18

Find the derivative of the following function. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 19

The future value that accrues when $200 is invested at 7%, compounded continuously, is   , where t is the number of years. At what rate is the money in this account growing when t = 7? Round your answer to the nearest cent.

Accepted Answer

A)  $1.63 per year 
B)  $326.46 per year 
C)  $15.02 per year 
D)  $2.15 per year 
E)  $22.85 per year 
A)  $1.63 per year 
B)  $326.46 per year 
C)  $15.02 per year 
D)  $2.15 per year 
E)  $22.85 per year

Question 20

Find the derivative of the following function. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Suppose that air is being pumped into a spherical balloon at a rate of 12 in³/min.At what rate is the radius of the balloon increasing when the radius is 9 in?

Between the years 1960 and 2002, the percent of women in the work force can be modeled by , where x is the number of years past 1950 (Source: U.S. Bureau of Labor Statistics). If this model is accurate beyond 2002, at what rate will the percent be changing in 2013?

Find .

For the given equation, find the slope of the tangent to the curve at the point . Round your answer to two decimal places.

Assume that x and y are differentiable functions of t. In each case, find given that , , and .

Find the derivative of the following function.

Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the radius of the tumor to decrease at a rate of 9 millimeters per month. At what rate is the surface area of the tumor decreasing when the radius is 2 mm?

Find the y-value at the relative minima, and use a graphing utility to check your result.

Suppose a 170-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 1 ft/sec, at what rate is the top of the ladder sliding down the wall when the bottom is 26 ft from the wall?

Find if .

If find y'.

Suppose that a company's sales volume y (in dollars) is related to its advertising expenditures x (in dollars) according to Find the rate of change of sales volume, with respect to advertising expenditures when x = $70. Round your answer to two decimal places.

Suppose that the revenue in dollars from the sale of x units of a product is given by . Find the marginal revenue function.

For many species of fish, the allometric relationship between the weight W and the length L is approximately where k is a constant. For find the percent rate of change of the weight as a corresponding percent rate of change of the length.

The radius of a circle is increasing at a rate of 6 ft/min. At what rate is its area changing when the radius is 7 ft?

The supply function for a product is given by , where x is the number of units supplied and p is the price in dollars. If the price is increasing at a rate of $1 per month, at what rate is the supply changing when Round your answer to three decimal places.

Find the derivative of the following function.

The future value that accrues when $200 is invested at 7%, compounded continuously, is , where t is the number of years. At what rate is the money in this account growing when t = 7? Round your answer to the nearest cent.

Find the derivative of the following function.

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Exam 11: Derivatives Continued

Suppose that air is being pumped into a spherical balloon at a rate of 12 in3/min.At what rate is the radius of the balloon increasing when the radius is 9 in?

Between the years 1960 and 2002, the percent of women in the work force can be modeled by , where x is the number of years past 1950 (Source: U.S. Bureau of Labor Statistics). If this model is accurate beyond 2002, at what rate will the percent be changing in 2013? ​

Find . ​ ​ ​

For the given equation, find the slope of the tangent to the curve at the point . Round your answer to two decimal places. ​ ​

Assume that x and y are differentiable functions of t. In each case, find given that , , and . ​ ​

Find the derivative of the following function. ​ ​

Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the radius of the tumor to decrease at a rate of 9 millimeters per month. At what rate is the surface area of the tumor decreasing when the radius is 2 mm? ​

Find the y-value at the relative minima, and use a graphing utility to check your result. ​ ​

Suppose a 170-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 1 ft/sec, at what rate is the top of the ladder sliding down the wall when the bottom is 26 ft from the wall? ​

Find if . ​

If find y'.

Suppose that a company's sales volume y (in dollars) is related to its advertising expenditures x (in dollars) according to Find the rate of change of sales volume, with respect to advertising expenditures when x = $70. Round your answer to two decimal places.

Suppose that the revenue in dollars from the sale of x units of a product is given by . Find the marginal revenue function. ​

For many species of fish, the allometric relationship between the weight W and the length L is approximately where k is a constant. For find the percent rate of change of the weight as a corresponding percent rate of change of the length. ​

The radius of a circle is increasing at a rate of 6 ft/min. At what rate is its area changing when the radius is 7 ft? ​

The supply function for a product is given by , where x is the number of units supplied and p is the price in dollars. If the price is increasing at a rate of $1 per month, at what rate is the supply changing when Round your answer to three decimal places. ​

Find the derivative of the following function. ​ ​

The future value that accrues when $200 is invested at 7%, compounded continuously, is , where t is the number of years. At what rate is the money in this account growing when t = 7? Round your answer to the nearest cent.

Find the derivative of the following function. ​ ​

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives

Indefinite Integrals

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

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Suppose that air is being pumped into a spherical balloon at a rate of 12 in³/min.At what rate is the radius of the balloon increasing when the radius is 9 in?

Between the years 1960 and 2002, the percent of women in the work force can be modeled by , where x is the number of years past 1950 (Source: U.S. Bureau of Labor Statistics). If this model is accurate beyond 2002, at what rate will the percent be changing in 2013?

Find .

For the given equation, find the slope of the tangent to the curve at the point . Round your answer to two decimal places.

Assume that x and y are differentiable functions of t. In each case, find given that , , and .

Find the derivative of the following function.

Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the radius of the tumor to decrease at a rate of 9 millimeters per month. At what rate is the surface area of the tumor decreasing when the radius is 2 mm?

Find the y-value at the relative minima, and use a graphing utility to check your result.

Suppose a 170-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 1 ft/sec, at what rate is the top of the ladder sliding down the wall when the bottom is 26 ft from the wall?

Find if .

Suppose that the revenue in dollars from the sale of x units of a product is given by . Find the marginal revenue function.

For many species of fish, the allometric relationship between the weight W and the length L is approximately where k is a constant. For find the percent rate of change of the weight as a corresponding percent rate of change of the length.

The radius of a circle is increasing at a rate of 6 ft/min. At what rate is its area changing when the radius is 7 ft?

The supply function for a product is given by , where x is the number of units supplied and p is the price in dollars. If the price is increasing at a rate of $1 per month, at what rate is the supply changing when Round your answer to three decimal places.

Find the derivative of the following function.

Find the derivative of the following function.