Question 1

For   find all real numbers a and b such that   exists.

Accepted Answer

A)    b any real number 
B)      
C)    b any real number 
D)      
A)    b any real number 
B)      
C)    b any real number 
D)

Question 2

Compute the derivative function f '(x) of   .

Accepted Answer

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

Question 3

A small company sold 1000 widgets this year at a price of $10 each. If the price increases at rate of $1.25 per year and the quantity sold increases at a rate of 250 widgets per year, at what rate will revenue increase?

Accepted Answer

A)  $312.5/year 
B)  $3750/year 
C)  $1250/year 
D)  $4062.5/year 
A)  $312.5/year 
B)  $3750/year 
C)  $1250/year 
D)  $4062.5/year

Question 4

Give the units for the derivative function.   represents the amount of a chemical present, in milligrams, at time t seconds.

Accepted Answer

A)  seconds per milligram 
B)  seconds per milligram squared 
C)  milligrams per second 
D)  milligrams per second squared 
A)  seconds per milligram 
B)  seconds per milligram squared 
C)  milligrams per second 
D)  milligrams per second squared

Question 5

Find the second derivative,   , of   .

Accepted Answer

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

Question 6

Compute the derivative function f '(x) of   .

Accepted Answer

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

Question 7

Estimate the slope of the tangent line to the curve at x = -2.

Accepted Answer

A)  -1 
B)  -2 
C)  2 
D)  0 
A)  -1 
B)  -2 
C)  2 
D)  0

Question 8

Find the derivative of   .

Accepted Answer

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

Question 9

Find an equation of the line tangent to   . (Round coefficients to 3 decimal places.)

Accepted Answer

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

Question 10

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 11

Determine the value(s) of x, if there are any, for which the slope of the tangent line to   does not exist.

Accepted Answer

A)    
B)      
C)      
D)  The slope exists for all values of x. 
A)    
B)      
C)      
D)  The slope exists for all values of x.

Question 12

Find a function   such that

Accepted Answer

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

Question 13

A weight hanging by a spring from the ceiling vibrates up and down. Its vertical position is given by   . Find the maximum speed of the weight and its position when it reaches maximum speed.

Accepted Answer

A)  speed = 4, position = 20 
B)  speed = 20, position = 0 
C)  speed = 5, position = 4 
D)  speed = 20, position = 5 
A)  speed = 4, position = 20 
B)  speed = 20, position = 0 
C)  speed = 5, position = 4 
D)  speed = 20, position = 5

Question 14

Find the location of all horizontal and vertical tangents for   .

Accepted Answer

A)  horizontal:   ; vertical: (-16, 0) 
B)  horizontal:   ; vertical: (0, 0) 
C)  horizontal:   ; vertical: none 
D)  horizontal:   ; vertical: (-16, 0) 
A)  horizontal:   ; vertical: (-16, 0) 
B)  horizontal:   ; vertical: (0, 0) 
C)  horizontal:   ; vertical: none 
D)  horizontal:   ; vertical: (-16, 0)

Question 15

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   . t
1995
2000
2005
2010   $1700
$2000
$2200
$2450

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 $50 per year. 
D)    ; The average monthly salary is increasing by $50 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 $50 per year. 
D)    ; The average monthly salary is increasing by $50 per year in 2010.

Question 16

Below is a graph of   . Sketch a plausible graph of a continuous function   .

Accepted Answer

Answers ma

Question 17

The height of an object at time t is given by   . Determine the object's acceleration at t = 2.

Accepted Answer

A)  10 
B)  4 
C)  9 
D)  -4 
A)  10 
B)  4 
C)  9 
D)  -4

Question 18

Find the derivative of   .

Accepted Answer

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

Question 19

Find the derivative of   .

Accepted Answer

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

Question 20

Find an equation of the line tangent to   at x = 3.

Accepted Answer

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

For find all real numbers a and b such that exists.

Compute the derivative function f '(x) of .

A small company sold 1000 widgets this year at a price of $10 each. If the price increases at rate of $1.25 per year and the quantity sold increases at a rate of 250 widgets per year, at what rate will revenue increase?

Give the units for the derivative function. represents the amount of a chemical present, in milligrams, at time t seconds.

Find the second derivative, , of .

Compute the derivative function f '(x) of .

Estimate the slope of the tangent line to the curve at x = -2.

Find the derivative of .

Find an equation of the line tangent to . (Round coefficients to 3 decimal places.)

Determine the value(s) of x, if there are any, for which the slope of the tangent line to does not exist.

Find a function such that

A weight hanging by a spring from the ceiling vibrates up and down. Its vertical position is given by . Find the maximum speed of the weight and its position when it reaches maximum speed.

Find the location of all horizontal and vertical tangents for .

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 . t 1995 2000 2005 2010 $1700 $2000 $2200 $2450

Below is a graph of . Sketch a plausible graph of a continuous function .

The height of an object at time t is given by . Determine the object's acceleration at t = 2.

Find the derivative of .

Find the derivative of .

Find an equation of the line tangent to at x = 3.

Preliminaries

Limits and Continuity

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

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

Exam 3: Differentiation

For find all real numbers a and b such that exists.

Compute the derivative function f '(x) of .

A small company sold 1000 widgets this year at a price of $10 each. If the price increases at rate of $1.25 per year and the quantity sold increases at a rate of 250 widgets per year, at what rate will revenue increase?

Give the units for the derivative function. represents the amount of a chemical present, in milligrams, at time t seconds.

Find the second derivative, , of .

Compute the derivative function f '(x) of .

Estimate the slope of the tangent line to the curve at x = -2.

Find the derivative of .

Find an equation of the line tangent to . (Round coefficients to 3 decimal places.)

Determine the value(s) of x, if there are any, for which the slope of the tangent line to does not exist.

Find a function such that

A weight hanging by a spring from the ceiling vibrates up and down. Its vertical position is given by . Find the maximum speed of the weight and its position when it reaches maximum speed.

Find the location of all horizontal and vertical tangents for .

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 . t 1995 2000 2005 2010 $1700 $2000 $2200 $2450

Below is a graph of . Sketch a plausible graph of a continuous function .

The height of an object at time t is given by . Determine the object's acceleration at t = 2.

Find the derivative of .

Find the derivative of .

Find an equation of the line tangent to at x = 3.

Preliminaries

Limits and Continuity

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

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