Question 1

​Find the derivative of the function. ​   ​

Accepted Answer

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

Question 2

​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 3

Find   of   ,   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  none of these choices 
A)    
B)    
C)    
D)    
E)  none of these choices

Question 4

​A population of bacteria is introduced into a culture.The number of bacteria P can be modeled by   where t is the time (in hours).Find the rate of change of the population when   ​

Accepted Answer

A)  36.98 bacteria/hr 
B)  ​29.15 bacteria/hr 
C)  ​33.65 bacteria/hr 
D)  ​32.75 bacteria/hr 
E)  ​30.25 bacteria/hr 
A)  36.98 bacteria/hr 
B)  ​29.15 bacteria/hr 
C)  ​33.65 bacteria/hr 
D)  ​32.75 bacteria/hr 
E)  ​30.25 bacteria/hr

Question 5

​Find the derivative of the following function using the limiting process. ​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​either B or D 
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​either B or D

Question 6

​The lengths of the edges of a cube are increasing at a rate of 4 ft/min.At what rate is the surface area changing when the edges are 21 ft long? ​

Accepted Answer

A)  ​96 ft2/min 
B)  1,008 ​ft2/min 
C)  504 ​ft2/min 
D)  ​2,016 ft2/min 
E)  ​84 ft2/min 
A)  ​96 ft2/min 
B)  1,008 ​ft2/min 
C)  504 ​ft2/min 
D)  ​2,016 ft2/min 
E)  ​84 ft2/min

Question 7

​Differentiate the given function. ​
​   ​

Accepted Answer

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

Question 8

​Boat docking.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 13   ,at what rate is the boat approaching the dock when it is 32 ft from the dock? Use the figure below. ​   ​

Accepted Answer

A)  16.25​   
B)  13​   
C)  ​21.67   
D)  ​9.75   
E)  ​7.8   
A)  16.25​   
B)  13​   
C)  ​21.67   
D)  ​9.75   
E)  ​7.8

Question 9

The cost C (in dollars)of producing x units of a product is given by   Find the additional cost when the production increases from 9 to 10.Round your answer to two decimal places. ​

Accepted Answer

A)  $0.58 
B)  $0.36 
C)  $0.62 
D)  $0.12 
E)  $0.64 
A)  $0.58 
B)  $0.36 
C)  $0.62 
D)  $0.12 
E)  $0.64

Question 10

​Find the derivative of the function. ​
​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​none of the above 
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​none of the above

Question 11

​Find the derivative of the function. ​
​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​none of the above 
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​none of the above

Question 12

​Assume that x and y are differentiable functions of t.Given   ,find   when   and   ​

Accepted Answer

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

Question 13

​The value V of a machine t years after it is purchased is inversely proportional to the square root of   The initial value of the machine is $10,000.Find the rate of depreciation when   Round your answer to two decimal places. ​

Accepted Answer

A)  -381.80 per year 
B)  ​-1,889.82 per year 
C)  ​447.21 per year 
D)  ​1,767.77 per year 
E)  -763.60​ per year 
A)  -381.80 per year 
B)  ​-1,889.82 per year 
C)  ​447.21 per year 
D)  ​1,767.77 per year 
E)  -763.60​ per year

Question 14

​Use the limit definition to find the slope of the tangent line to the graph of   at the point   ​

Accepted Answer

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

Question 15

​Find   for the equation   ​

Accepted Answer

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

Question 16

​Find the marginal revenue for producing x units.(The revenue is measured in dollars.) ​   ​

Accepted Answer

A)  ​   dollars 
B)  ​​   dollars 
C)  ​​50 dollars 
D)  ​​   dollars 
E)  ​​​   dollars 
A)  ​   dollars 
B)  ​​   dollars 
C)  ​​50 dollars 
D)  ​​   dollars 
E)  ​​​   dollars

Question 17

​Area.The radius,r,of a circle is decreasing at a rate of 4 centimeters per minute. Find the rate of change of area,A,when the radius is 6.
​

Accepted Answer

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

Question 18

Find the third derivative. ​   ​

Accepted Answer

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

Question 19

A point is moving along the graph of the function   such that   centimeters per second. Find   when   ​

Accepted Answer

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

Question 20

​Find the derivative of the function   ​

Accepted Answer

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

Find the derivative of the function.

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

Find of ,

A population of bacteria is introduced into a culture.The number of bacteria P can be modeled by where t is the time (in hours).Find the rate of change of the population when

Find the derivative of the following function using the limiting process.

The lengths of the edges of a cube are increasing at a rate of 4 ft/min.At what rate is the surface area changing when the edges are 21 ft long?

Differentiate the given function.

Boat docking.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 13 ,at what rate is the boat approaching the dock when it is 32 ft from the dock? Use the figure below.

The cost C (in dollars)of producing x units of a product is given by Find the additional cost when the production increases from 9 to 10.Round your answer to two decimal places.

Find the derivative of the function.

Find the derivative of the function.

Assume that x and y are differentiable functions of t.Given ,find when and

The value V of a machine t years after it is purchased is inversely proportional to the square root of The initial value of the machine is $10,000.Find the rate of depreciation when Round your answer to two decimal places.

Use the limit definition to find the slope of the tangent line to the graph of at the point

Find for the equation

Find the marginal revenue for producing x units.(The revenue is measured in dollars.)

Area.The radius,r,of a circle is decreasing at a rate of 4 centimeters per minute. Find the rate of change of area,A,when the radius is 6.

Find the third derivative.

A point is moving along the graph of the function such that centimeters per second. Find when

Find the derivative of the function

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

​Find the derivative of the function. ​ ​

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

Find of , ​

​A population of bacteria is introduced into a culture.The number of bacteria P can be modeled by where t is the time (in hours).Find the rate of change of the population when ​

​Find the derivative of the following function using the limiting process. ​ ​

​The lengths of the edges of a cube are increasing at a rate of 4 ft/min.At what rate is the surface area changing when the edges are 21 ft long? ​

​Differentiate the given function. ​ ​ ​

​Boat docking.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 13 ,at what rate is the boat approaching the dock when it is 32 ft from the dock? Use the figure below. ​ ​

The cost C (in dollars)of producing x units of a product is given by Find the additional cost when the production increases from 9 to 10.Round your answer to two decimal places. ​

​Find the derivative of the function. ​ ​ ​

​Find the derivative of the function. ​ ​ ​

​Assume that x and y are differentiable functions of t.Given ,find when and ​

​The value V of a machine t years after it is purchased is inversely proportional to the square root of The initial value of the machine is $10,000.Find the rate of depreciation when Round your answer to two decimal places. ​

​Use the limit definition to find the slope of the tangent line to the graph of at the point ​

​Find for the equation ​

​Find the marginal revenue for producing x units.(The revenue is measured in dollars.) ​ ​

​Area.The radius,r,of a circle is decreasing at a rate of 4 centimeters per minute. Find the rate of change of area,A,when the radius is 6. ​

Find the third derivative. ​ ​

A point is moving along the graph of the function such that centimeters per second. Find when ​

​Find the derivative of the function ​

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

Find the derivative of the function.

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

Find of ,

A population of bacteria is introduced into a culture.The number of bacteria P can be modeled by where t is the time (in hours).Find the rate of change of the population when

Find the derivative of the following function using the limiting process.

The lengths of the edges of a cube are increasing at a rate of 4 ft/min.At what rate is the surface area changing when the edges are 21 ft long?

Differentiate the given function.

Boat docking.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 13 ,at what rate is the boat approaching the dock when it is 32 ft from the dock? Use the figure below.

The cost C (in dollars)of producing x units of a product is given by Find the additional cost when the production increases from 9 to 10.Round your answer to two decimal places.

Find the derivative of the function.

Find the derivative of the function.

Assume that x and y are differentiable functions of t.Given ,find when and

The value V of a machine t years after it is purchased is inversely proportional to the square root of The initial value of the machine is $10,000.Find the rate of depreciation when Round your answer to two decimal places.

Use the limit definition to find the slope of the tangent line to the graph of at the point

Find for the equation

Find the marginal revenue for producing x units.(The revenue is measured in dollars.)

Area.The radius,r,of a circle is decreasing at a rate of 4 centimeters per minute. Find the rate of change of area,A,when the radius is 6.

Find the third derivative.

A point is moving along the graph of the function such that centimeters per second. Find when

Find the derivative of the function