Question 1

​A point is moving along the graph of the function   such that   centimeters per second. Find   for the given values of x.
​   ​

Accepted Answer

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

Question 2

​Find the   of   ​

Accepted Answer

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

Question 3

​Let x represent the units of labor and y the capital invested in a manufacturing process.When 135,540 units are produced,the relationship between labor and capital can be modeled by   Find the rate of change of y with respect to x when   and   ​

Accepted Answer

A)  ​-2 
B)  ​0 
C)  ​3 
D)  ​-7 
E)  ​5 
A)  ​-2 
B)  ​0 
C)  ​3 
D)  ​-7 
E)  ​5

Question 4

​Find the derivative of the function   ​

Accepted Answer

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

Question 5

​Find   implicitly and explicitly(the explicit functions are shown on the graph)and show that the results are equivalent.Use the graph to estimate the slope of the tangent line at the labeled point.Then verify your result analytically by evaluating   at the point. ​   ​   ​

Accepted Answer

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

Question 6

The radius r of a sphere is increasing at a rate of 5 inches per minute.Find the rate of change of volume when   inches.Round your answer to one decimal place. ​

Accepted Answer

A)  1,809.6 cubic inches per minute 
B)  7,238.2 cubic inches per minute 
C)  36,191.1 cubic inches per minute 
D)  9,047.8 cubic inches per minute 
E)  27,143.4 cubic inches per minute 
A)  1,809.6 cubic inches per minute 
B)  7,238.2 cubic inches per minute 
C)  36,191.1 cubic inches per minute 
D)  9,047.8 cubic inches per minute 
E)  27,143.4 cubic inches per minute

Question 7

​Find the point(s),if any,at which the graph of f has a horizontal tangent line. ​   ​

Accepted Answer

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

Question 8

​The profit (in dollars)from selling x units of calculus textbooks is given by   Find the additional profit when the sales increase from 146 to 147 units.Round your answer to two decimal places. ​

Accepted Answer

A)  ​$15.35 
B)  ​$30.00 
C)  ​$15.45 
D)  ​$30.80 
E)  ​$30.60 
A)  ​$15.35 
B)  ​$30.00 
C)  ​$15.45 
D)  ​$30.80 
E)  ​$30.60

Question 9

​Volume and radius.Suppose that air is being pumped into a spherical balloon at a rate of 8 in.3/min.At what rate is the radius of the balloon increasing when the radius is 7 in.? ​

Accepted Answer

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

Question 10

​Find the derivative of the function. ​
​   ​

Accepted Answer

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

Question 11

​Use the product Rule to find the derivative of the function   ​

Accepted Answer

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

Question 12

​Find the slope of the graph at the given point. ​   ​   ​

Accepted Answer

A)  ​0 
B)  ​3 
C)  ​5 
D)  ​4 
E)  ​7 
A)  ​0 
B)  ​3 
C)  ​5 
D)  ​4 
E)  ​7

Question 13

When the price of a glass of lemonade at a lemonade stand was $1.75,400 glasses were sold.When the price was lowered to $1.50,500 glasses were sold.Assume that the demand function is linear and that the marginal and fixed costs are $0.10 and $ 25,respectively.Find the marginal profit when 300 glasses of lemonade are sold and when 700 glasses of lemonade are sold. ​

Accepted Answer

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

Question 14

Differentiate the given function. ​   ​

Accepted Answer

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

Question 15

Find the derivative of the given function. ​   ​

Accepted Answer

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

Question 16

​Find an equation of the tangent line to the graph of f at the given point. ​   ,at   ​

Accepted Answer

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

Question 17

​Find   ,   ,and   of the functions   ,   ​

Accepted Answer

A)  ​   ,   , and   
B)  ​​   ,   , and   
C)  ​​   ,   , and   
D)  ​​   ,   , and   
E)  ​​   ,   ,and   
A)  ​   ,   , and   
B)  ​​   ,   , and   
C)  ​​   ,   , and   
D)  ​​   ,   , and   
E)  ​​   ,   ,and

Question 18

Find the derivative of the function. ​
​   ​

Accepted Answer

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

Question 19

​Assume that x and y are differentiable functions of t.Find   using the given values. ​   for   ,   ​

Accepted Answer

A)  ​216 
B)  ​82 
C)  ​164 
D)  ​214 
E)  ​107 
A)  ​216 
B)  ​82 
C)  ​164 
D)  ​214 
E)  ​107

Question 20

​Use the given information to find   of the function   ​   ,   ,   and   ​

Accepted Answer

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

A point is moving along the graph of the function such that centimeters per second. Find for the given values of x.

Find the of

Let x represent the units of labor and y the capital invested in a manufacturing process.When 135,540 units are produced,the relationship between labor and capital can be modeled by Find the rate of change of y with respect to x when and

Find the derivative of the function

Find implicitly and explicitly(the explicit functions are shown on the graph)and show that the results are equivalent.Use the graph to estimate the slope of the tangent line at the labeled point.Then verify your result analytically by evaluating at the point.

The radius r of a sphere is increasing at a rate of 5 inches per minute.Find the rate of change of volume when inches.Round your answer to one decimal place.

Find the point(s),if any,at which the graph of f has a horizontal tangent line.

The profit (in dollars)from selling x units of calculus textbooks is given by Find the additional profit when the sales increase from 146 to 147 units.Round your answer to two decimal places.

Volume and radius.Suppose that air is being pumped into a spherical balloon at a rate of 8 in.³/min.At what rate is the radius of the balloon increasing when the radius is 7 in.?

Find the derivative of the function.

Use the product Rule to find the derivative of the function

Find the slope of the graph at the given point.

Differentiate the given function.

Find the derivative of the given function.

Find an equation of the tangent line to the graph of f at the given point. ,at

Find , ,and of the functions ,

Find the derivative of the function.

Assume that x and y are differentiable functions of t.Find using the given values. for ,

Use the given information to find of the function , , and

Functions, graphs, and Limits

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

Exam 2: Differentiation

​A point is moving along the graph of the function such that centimeters per second. Find for the given values of x. ​ ​

​Find the of ​

​Let x represent the units of labor and y the capital invested in a manufacturing process.When 135,540 units are produced,the relationship between labor and capital can be modeled by Find the rate of change of y with respect to x when and ​

​Find the derivative of the function ​

​Find implicitly and explicitly(the explicit functions are shown on the graph)and show that the results are equivalent.Use the graph to estimate the slope of the tangent line at the labeled point.Then verify your result analytically by evaluating at the point. ​ ​ ​

The radius r of a sphere is increasing at a rate of 5 inches per minute.Find the rate of change of volume when inches.Round your answer to one decimal place. ​

​Find the point(s),if any,at which the graph of f has a horizontal tangent line. ​ ​

​The profit (in dollars)from selling x units of calculus textbooks is given by Find the additional profit when the sales increase from 146 to 147 units.Round your answer to two decimal places. ​

​Volume and radius.Suppose that air is being pumped into a spherical balloon at a rate of 8 in.3/min.At what rate is the radius of the balloon increasing when the radius is 7 in.? ​

​Find the derivative of the function. ​ ​ ​

​Use the product Rule to find the derivative of the function ​

​Find the slope of the graph at the given point. ​ ​ ​

Differentiate the given function. ​ ​

Find the derivative of the given function. ​ ​

​Find an equation of the tangent line to the graph of f at the given point. ​ ,at ​

​Find , ,and of the functions , ​

Find the derivative of the function. ​ ​ ​

​Assume that x and y are differentiable functions of t.Find using the given values. ​ for , ​

​Use the given information to find of the function ​ , , and ​

Functions, graphs, and Limits

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

A point is moving along the graph of the function such that centimeters per second. Find for the given values of x.

Find the of

Let x represent the units of labor and y the capital invested in a manufacturing process.When 135,540 units are produced,the relationship between labor and capital can be modeled by Find the rate of change of y with respect to x when and

Find the derivative of the function

Find implicitly and explicitly(the explicit functions are shown on the graph)and show that the results are equivalent.Use the graph to estimate the slope of the tangent line at the labeled point.Then verify your result analytically by evaluating at the point.

The radius r of a sphere is increasing at a rate of 5 inches per minute.Find the rate of change of volume when inches.Round your answer to one decimal place.

Find the point(s),if any,at which the graph of f has a horizontal tangent line.

The profit (in dollars)from selling x units of calculus textbooks is given by Find the additional profit when the sales increase from 146 to 147 units.Round your answer to two decimal places.

Volume and radius.Suppose that air is being pumped into a spherical balloon at a rate of 8 in.³/min.At what rate is the radius of the balloon increasing when the radius is 7 in.?

Find the derivative of the function.

Use the product Rule to find the derivative of the function

Find the slope of the graph at the given point.

Differentiate the given function.

Find the derivative of the given function.

Find an equation of the tangent line to the graph of f at the given point. ,at

Find , ,and of the functions ,

Find the derivative of the function.

Assume that x and y are differentiable functions of t.Find using the given values. for ,

Use the given information to find of the function , , and