Question 1

For the given pair of functions, write the composite function and its derivative in terms of one input variable.

Accepted Answer

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

Question 2

Find the derivative of

Accepted Answer

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

Question 3

Differentiate the given function.

Accepted Answer

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

Question 4

A publishing company estimates that when a new book by a best-selling American author first hits the market, its sales can be predicted by the equation   , where   represents the total number (in thousands) of copies of the book sold in the United States by the end of the xth week. The number of copies of the book sold abroad by the end of the xth week can be modeled by   thousand copies of the book How many books will be sold by the end of the first year (that is, 52 weeks)?

Accepted Answer

A)  497,278 books 
B)  503,778 books 
C)  6,500 books 
D)  490,778 books 
E)  4,907 books 
A)  497,278 books 
B)  503,778 books 
C)  6,500 books 
D)  490,778 books 
E)  4,907 books

Question 5

For the given pair of functions, write the composite function and its derivative in terms of one input variable.

Accepted Answer

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

Question 6

Find the derivative of

Accepted Answer

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

Question 7

Find   of   by using the definition of the derivative.

Accepted Answer

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

Question 8

Suppose the percentage of children living with their grandparents between 1970 and 2000 can be modeled by the equation   percent, t years after 1970. How rapidly on average did the percentage of children living with their grandparents grow between 1974 and 1993?

Accepted Answer

A)  24.01 % per year 
B)  14.06 % per year 
C)  16.98 % per year 
D)  9.95 % per year 
E)  2.92 % per year 
A)  24.01 % per year 
B)  14.06 % per year 
C)  16.98 % per year 
D)  9.95 % per year 
E)  2.92 % per year

Question 9

Using the product rule write the rate-of-change function.

Accepted Answer

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

Question 10

The number of private donations received by nongovernment disaster relief organizations can be modeled as   thousand donations where x is the number of hours since a major disaster has struck. At what time is the rate of change of donations zero?
Round to the nearest thousandth.

Accepted Answer

A)  12.346 hours 
B)  0.111 hours 
C)  1.111 hours 
D)  0.992 hours 
E)  11.111 hours 
A)  12.346 hours 
B)  0.111 hours 
C)  1.111 hours 
D)  0.992 hours 
E)  11.111 hours

Question 11

The managers of a company have modeled some cost data and found that if they produce x storm windows each hour, the cost (in dollars) to produce one window is given by the function   , for   . The company sells its storm windows for $190 each. Assuming that every window made will be sold, give a formula for the profit made from the sale of one storm window when the company is producing x windows each hour.

Accepted Answer

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

Question 12

Find the derivative of   .

Accepted Answer

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

Question 13

Calculate the derivative of the function with the appropriate formula.

Accepted Answer

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

Question 14

Find the derivative of   .

Accepted Answer

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

Question 15

For each of the composite functions, identify an inside function and an outside function and write the derivative with respect to x of the composite function.

Accepted Answer

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

Question 16

Using the product rule write the rate-of-change function.

Accepted Answer

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

Question 17

The population of Aurora, a Nevada ghost town, can be modeled as   where output is measured in people and t is the number of years since 1859. Write a model for the rate of change of the population of Aurora.

Accepted Answer

A)    where output is measured in people per year gives the rate of change of the population of Aurora, Nevada t years since 1859. 
B)    where output is measured in people per year gives the rate of change of the population of Aurora, Nevada t years since 1859. 
C)    where output is measured in people per year gives the rate of change of the population of Aurora, Nevada t years since 1859. 
D)    where output is measured in people per year gives the rate of change of the population of Aurora, Nevada t years since 1859. 
E)    where output is measured in people per year gives the rate of change of the population of Aurora, Nevada t years since 1859. 
A)    where output is measured in people per year gives the rate of change of the population of Aurora, Nevada t years since 1859. 
B)    where output is measured in people per year gives the rate of change of the population of Aurora, Nevada t years since 1859. 
C)    where output is measured in people per year gives the rate of change of the population of Aurora, Nevada t years since 1859. 
D)    where output is measured in people per year gives the rate of change of the population of Aurora, Nevada t years since 1859. 
E)    where output is measured in people per year gives the rate of change of the population of Aurora, Nevada t years since 1859.

Question 18

Evaluate   where   given   ,   ,   ,   .

Accepted Answer

A)  -13.5 
B)  -10 
C)  9 
D)  19 
E)  -19 
A)  -13.5 
B)  -10 
C)  9 
D)  19 
E)  -19

Question 19

Evaluate the limit   using L'Hôpital's Rule, if necessary.

Accepted Answer

A)      
B)    
C)  0 
D)    
E)    
A)      
B)    
C)  0 
D)    
E)

Question 20

Use L'Hôpital's Rule to find the limit.

Accepted Answer

A)    
B)  0 
C)    
D)    
E)  Limit does not exist. 
A)    
B)  0 
C)    
D)    
E)  Limit does not exist.

For the given pair of functions, write the composite function and its derivative in terms of one input variable.

Find the derivative of

Differentiate the given function.

For the given pair of functions, write the composite function and its derivative in terms of one input variable.

Find the derivative of

Find of by using the definition of the derivative.

Suppose the percentage of children living with their grandparents between 1970 and 2000 can be modeled by the equation percent, t years after 1970. How rapidly on average did the percentage of children living with their grandparents grow between 1974 and 1993?

Using the product rule write the rate-of-change function.

The number of private donations received by nongovernment disaster relief organizations can be modeled as thousand donations where x is the number of hours since a major disaster has struck. At what time is the rate of change of donations zero? Round to the nearest thousandth.

Find the derivative of .

Calculate the derivative of the function with the appropriate formula.

Find the derivative of .

For each of the composite functions, identify an inside function and an outside function and write the derivative with respect to x of the composite function.

Using the product rule write the rate-of-change function.

The population of Aurora, a Nevada ghost town, can be modeled as where output is measured in people and t is the number of years since 1859. Write a model for the rate of change of the population of Aurora.

Evaluate where given , , , .

Evaluate the limit using L'Hôpital's Rule, if necessary.

Use L'Hôpital's Rule to find the limit.

Ingredients of Change: Functions an Limits

Describing Change: Rates

Analyzing Change: Applications of Derivatives

Accumulating Change: Limits of Sums and the Definite Integral

Analyzing Accumulated Change: Integrals in Action

Ingredients of Multivariable Change: Models, Graphs, Rates

Analyzing Multivariable Change: Optimization

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Exam 3: Determining Change: Derivatives

For the given pair of functions, write the composite function and its derivative in terms of one input variable.

Find the derivative of

Differentiate the given function.

For the given pair of functions, write the composite function and its derivative in terms of one input variable.

Find the derivative of

Find of by using the definition of the derivative.

Suppose the percentage of children living with their grandparents between 1970 and 2000 can be modeled by the equation percent, t years after 1970. How rapidly on average did the percentage of children living with their grandparents grow between 1974 and 1993?

Using the product rule write the rate-of-change function.

The number of private donations received by nongovernment disaster relief organizations can be modeled as thousand donations where x is the number of hours since a major disaster has struck. At what time is the rate of change of donations zero? Round to the nearest thousandth.

Find the derivative of .

Calculate the derivative of the function with the appropriate formula.

Find the derivative of .

For each of the composite functions, identify an inside function and an outside function and write the derivative with respect to x of the composite function.

Using the product rule write the rate-of-change function.

The population of Aurora, a Nevada ghost town, can be modeled as where output is measured in people and t is the number of years since 1859. Write a model for the rate of change of the population of Aurora.

Evaluate where given , , , .

Evaluate the limit using L'Hôpital's Rule, if necessary.

Use L'Hôpital's Rule to find the limit.

Ingredients of Change: Functions an Limits

Describing Change: Rates

Analyzing Change: Applications of Derivatives

Accumulating Change: Limits of Sums and the Definite Integral

Analyzing Accumulated Change: Integrals in Action

Ingredients of Multivariable Change: Models, Graphs, Rates

Analyzing Multivariable Change: Optimization

Filters