Question 1

Find the derivative of   .

Accepted Answer

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

Question 2

Find the derivative of   .

Accepted Answer

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

Question 3

Differentiate the function.

Accepted Answer

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

Question 4

Let   equal the average monthly salary of families in a certain city in year t. Several values are given in the table below. Estimate and interpret   .

Accepted Answer

A)    ; The rate at which the average monthly salary is increasing each year in 2010 is increasing by $2 per year. 
B)    ; The average monthly salary is increasing by $2 per year in 2010. 
C)    ; The rate at which the average monthly salary is increasing each year in 2010 is increasing by $30 per year. 
D)    ; The average monthly salary is increasing by $30 per year in 2010. 
A)    ; The rate at which the average monthly salary is increasing each year in 2010 is increasing by $2 per year. 
B)    ; The average monthly salary is increasing by $2 per year in 2010. 
C)    ; The rate at which the average monthly salary is increasing each year in 2010 is increasing by $30 per year. 
D)    ; The average monthly salary is increasing by $30 per year in 2010.

Question 5

Use the position function   feet to find the velocity at t = 3 seconds. (Round answer to 2 decimal places.)

Accepted Answer

A)  v(3) = -5.44 ft/s 
B)  v(3) = -6.56 ft/s 
C)  v(3) = 6.56 ft/s 
D)  v(3) = -7.92 ft/s 
A)  v(3) = -5.44 ft/s 
B)  v(3) = -6.56 ft/s 
C)  v(3) = 6.56 ft/s 
D)  v(3) = -7.92 ft/s

Question 6

Find the derivative   implicitly if   .

Accepted Answer

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

Question 7

Using the position function   , find the velocity function.

Accepted Answer

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

Question 8

The value of an investment is given by   . Find the instantaneous percentage rate of change. (Round to 2 decimal places.)

Accepted Answer

A)  1.39 % per year 
B)  33.27 % per year 
C)  138.63 % per year 
D)  17.31 % per year 
A)  1.39 % per year 
B)  33.27 % per year 
C)  138.63 % per year 
D)  17.31 % per year

Question 9

Find an equation of the tangent line to y = f(x) at x = 3.

Accepted Answer

A)  y = -12x - 36 
B)  y = 34x + 63 
C)  y = 12x - 36 
D)  y = 34x - 63 
A)  y = -12x - 36 
B)  y = 34x + 63 
C)  y = 12x - 36 
D)  y = 34x - 63

Question 10

Sketch the graph of the function.

Accepted Answer

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

Question 11

The table shows the temperature in degrees Celsius at various distances, d in feet, from a specified point. Estimate the slope of the tangent line at   and interpret the result.

Accepted Answer

A)    The temperature is increasing 4.67   per foot at the point 2 feet from the specified point. 
B)    The temperature is decreasing 0.33   per foot at the point 2 feet from the specified point. 
C)    The temperature is decreasing 3   per foot at the point 2 feet from the specified point. 
D)    The temperature is increasing 20   per foot at the point 2 feet from the specified point. 
A)    The temperature is increasing 4.67   per foot at the point 2 feet from the specified point. 
B)    The temperature is decreasing 0.33   per foot at the point 2 feet from the specified point. 
C)    The temperature is decreasing 3   per foot at the point 2 feet from the specified point. 
D)    The temperature is increasing 20   per foot at the point 2 feet from the specified point.

Question 12

The height of an object at time t is given by   . Determine the object's acceleration at t = 3.

Accepted Answer

A)  60 
B)  16 
C)  44 
D)  -16 
A)  60 
B)  16 
C)  44 
D)  -16

Question 13

Prove that   has exactly one solution.

Accepted Answer

Let @#IMG-DLM& . The function f(x) is continuous a

Question 14

Find the derivative of   .

Accepted Answer

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

Question 15

Find the derivative of the function.

Accepted Answer

The answer of Find the derivative of the function. ...

Question 16

Find a function with the given derivative.

Accepted Answer

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

Question 17

Differentiate the function.

Accepted Answer

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

Question 18

Use the position function   meters to find the velocity at t = 4 seconds.

Accepted Answer

A)  8 m/s 
B)    m/s 
C)    m/s 
D)    m/s 
A)  8 m/s 
B)    m/s 
C)    m/s 
D)    m/s

Question 19

The graph below gives distance in miles from a starting point as a function of time in hours for a car on a trip. Find the fastest speed (magnitude of velocity) during the trip. Describe how the speed during the first 2 hours compares to the speed during the last 2 hours. Describe what is happening between 2 and 3 hours.

Accepted Answer

The fastest speed occurred during the la

Question 20

The table below gives the position s(t) for a car beginning at a point and returning 5 hours later. Estimate the velocity v(t) at two points around the third hour.

Accepted Answer

The velocity is the change in distance t

Find the derivative of .

Find the derivative of .

Differentiate the function.

Let equal the average monthly salary of families in a certain city in year t. Several values are given in the table below. Estimate and interpret .

Use the position function feet to find the velocity at t = 3 seconds. (Round answer to 2 decimal places.)

Find the derivative implicitly if .

Using the position function , find the velocity function.

The value of an investment is given by . Find the instantaneous percentage rate of change. (Round to 2 decimal places.)

Find an equation of the tangent line to y = f(x) at x = 3.

Sketch the graph of the function.

The table shows the temperature in degrees Celsius at various distances, d in feet, from a specified point. Estimate the slope of the tangent line at and interpret the result.

The height of an object at time t is given by . Determine the object's acceleration at t = 3.

Prove that has exactly one solution.

Find the derivative of .

Find the derivative of the function.

Find a function with the given derivative.

Differentiate the function.

Use the position function meters to find the velocity at t = 4 seconds.

The table below gives the position s(t) for a car beginning at a point and returning 5 hours later. Estimate the velocity v(t) at two points around the third hour.

Preliminaries

Limits and Continuity

Applications of the Derivative

Integration

Applications of the Definite Integral

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

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Exam 3: Differentiation

Find the derivative of .

Find the derivative of .

Differentiate the function.

Let equal the average monthly salary of families in a certain city in year t. Several values are given in the table below. Estimate and interpret .

Use the position function feet to find the velocity at t = 3 seconds. (Round answer to 2 decimal places.)

Find the derivative implicitly if .

Using the position function , find the velocity function.

The value of an investment is given by . Find the instantaneous percentage rate of change. (Round to 2 decimal places.)

Find an equation of the tangent line to y = f(x) at x = 3.

Sketch the graph of the function.

The table shows the temperature in degrees Celsius at various distances, d in feet, from a specified point. Estimate the slope of the tangent line at and interpret the result.

The height of an object at time t is given by . Determine the object's acceleration at t = 3.

Prove that has exactly one solution.

Find the derivative of .

Find the derivative of the function.

Find a function with the given derivative.

Differentiate the function.

Use the position function meters to find the velocity at t = 4 seconds.

The table below gives the position s(t) for a car beginning at a point and returning 5 hours later. Estimate the velocity v(t) at two points around the third hour.

Preliminaries

Limits and Continuity

Applications of the Derivative

Integration

Applications of the Definite Integral

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters