Question 1

Find the slope of the graph of the function at the given value. ​   at   ​

Accepted Answer

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

Question 2

Find the derivative of the function. ​   ​

Accepted Answer

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

Question 3

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

Accepted Answer

A) -3 
B)    
C)    
D)    
E)    
A) -3 
B)    
C)    
D)    
E)

Question 4

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

Accepted Answer

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

Question 5

​For what positive value of   does the tangent line to the curve   intersect the   -axis at the point   ? ​

Accepted Answer

A) ​4.076 
B) 3.375 
C) ​3.638 
D) 4.383 
A) ​4.076 
B) 3.375 
C) ​3.638 
D) 4.383

Question 6

A point is moving along the graph of the function   such that   centimeters per second.Find   when x = 1. ​

Accepted Answer

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

Question 7

Use implicit differentiation to find   at the point   . ​   ​

Accepted Answer

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

Question 8

Find the derivative of the function   .Simplify your answer. ​

Accepted Answer

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

Question 9

Determine all values of x, (if any),at which the graph of the function has a horizontal tangent. ​   ​

Accepted Answer

A)    and   
B)    
C)    and   
D)    
E) The graph has no horizontal tangents. 
A)    and   
B)    
C)    and   
D)    
E) The graph has no horizontal tangents.

Question 10

Find the rate of change of the distance D between the origin and a moving point on the graph of   if   centimeters per second. ​

Accepted Answer

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

Question 11

Suppose that an automobile's velocity starting from rest is   where v is measured in feet per second.Find the acceleration at 7 seconds.Round your answer to one decimal place. ​

Accepted Answer

A) 1.6   
B) 0.7   
C) 0.4   
D) 0.2   
E) 5.1   
A) 1.6   
B) 0.7   
C) 0.4   
D) 0.2   
E) 5.1

Question 12

Find   in terms of x and y. ​   ​

Accepted Answer

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

Question 13

Find an equation of the tangent line to the graph of the function   at the point   . ​​

Accepted Answer

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

Question 14

Evaluate   for the equation   at the given point   .Round your answer to two decimal places if necessary. ​

Accepted Answer

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

Question 15

Evaluate the derivative of the function   at the point   . ​

Accepted Answer

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

Question 16

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 17

Differentiate the function   . ​

Accepted Answer

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

Question 18

Differentiate the function   . ​

Accepted Answer

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

Question 19

Find the derivative of the function   . ​

Accepted Answer

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

Question 20

Use implicit differentiation to find an equation of the tangent line to the ellipse   at   . ​

Accepted Answer

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

Find the slope of the graph of the function at the given value. at

Find the derivative of the function.

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

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

For what positive value of does the tangent line to the curve intersect the -axis at the point ?

A point is moving along the graph of the function such that centimeters per second.Find when x = 1.

Use implicit differentiation to find at the point .

Find the derivative of the function .Simplify your answer.

Determine all values of x, (if any),at which the graph of the function has a horizontal tangent.

Find the rate of change of the distance D between the origin and a moving point on the graph of if centimeters per second.

Suppose that an automobile's velocity starting from rest is where v is measured in feet per second.Find the acceleration at 7 seconds.Round your answer to one decimal place.

Find in terms of x and y.

Find an equation of the tangent line to the graph of the function at the point .

Evaluate for the equation at the given point .Round your answer to two decimal places if necessary.

Evaluate the derivative of the function at the point .

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

Differentiate the function .

Differentiate the function .

Find the derivative of the function .

Use implicit differentiation to find an equation of the tangent line to the ellipse at .

Preparation for Calculus

Limits and Their Properties

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Exam 3: Differentiation

Find the slope of the graph of the function at the given value. ​ at ​

Find the derivative of the function. ​ ​

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

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

​For what positive value of does the tangent line to the curve intersect the -axis at the point ? ​

A point is moving along the graph of the function such that centimeters per second.Find when x = 1. ​

Use implicit differentiation to find at the point . ​ ​

Find the derivative of the function .Simplify your answer. ​

Determine all values of x, (if any),at which the graph of the function has a horizontal tangent. ​ ​

Find the rate of change of the distance D between the origin and a moving point on the graph of if centimeters per second. ​

Suppose that an automobile's velocity starting from rest is where v is measured in feet per second.Find the acceleration at 7 seconds.Round your answer to one decimal place. ​

Find in terms of x and y. ​ ​

Find an equation of the tangent line to the graph of the function at the point . ​​

Evaluate for the equation at the given point .Round your answer to two decimal places if necessary. ​

Evaluate the derivative of the function at the point . ​

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

Differentiate the function . ​

Differentiate the function . ​

Find the derivative of the function . ​

Use implicit differentiation to find an equation of the tangent line to the ellipse at . ​

Preparation for Calculus

Limits and Their Properties

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Find the slope of the graph of the function at the given value. at

Find the derivative of the function.

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

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

For what positive value of does the tangent line to the curve intersect the -axis at the point ?

A point is moving along the graph of the function such that centimeters per second.Find when x = 1.

Use implicit differentiation to find at the point .

Find the derivative of the function .Simplify your answer.

Determine all values of x, (if any),at which the graph of the function has a horizontal tangent.

Find the rate of change of the distance D between the origin and a moving point on the graph of if centimeters per second.

Suppose that an automobile's velocity starting from rest is where v is measured in feet per second.Find the acceleration at 7 seconds.Round your answer to one decimal place.

Find in terms of x and y.

Find an equation of the tangent line to the graph of the function at the point .

Evaluate for the equation at the given point .Round your answer to two decimal places if necessary.

Evaluate the derivative of the function at the point .

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

Differentiate the function .

Differentiate the function .

Find the derivative of the function .

Use implicit differentiation to find an equation of the tangent line to the ellipse at .