Question 1

​Find an equation of the line that passes through the point   and has the slope m that is undefined. ​

Accepted Answer

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

Question 2

​Find the x-value at which the given function has a point of inflection. ​
​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​no point of inflection 
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​no point of inflection

Question 3

​Volume.A rectangular box with a square base is to be formed from a square piece of metal with 54-inch sides.If a square piece with side x is cut from each corner of the metal and the sides are folded up to form an open box,the volume of the box is   What value of x will maximize the volume of the box? ​   ​

Accepted Answer

A)  ​27 
B)  ​2 
C)  ​9 
D)  ​14 
E)  ​1 
A)  ​27 
B)  ​2 
C)  ​9 
D)  ​14 
E)  ​1

Question 4

​Find   ​

Accepted Answer

A)  ​-3 
B)  ​0 
C)  ​-∞ 
D)  ​3 
E)  ​∞ 
A)  ​-3 
B)  ​0 
C)  ​-∞ 
D)  ​3 
E)  ​∞

Question 5

​If the total cost function for a product is   dollars.Find the minimum average cost. ​

Accepted Answer

A)  ​$14.25 per unit 
B)  $​18 per unit 
C)  ​$14.36 per unit 
D)  ​$14 per unit 
E)  ​$13 per unit 
A)  ​$14.25 per unit 
B)  $​18 per unit 
C)  ​$14.36 per unit 
D)  ​$14 per unit 
E)  ​$13 per unit

Question 6

​Determine the open intervals on which the graph of   is concave downward or concave upward. ​

Accepted Answer

A)  ​concave downward on   
B)  ​concave downward on   ; concave upward on   
C)  ​concave upward on   ; concave downward on   
D)  ​​concave downward on   ; ​concave upward on   
E)  ​concave upward on   ; concave downward on   
A)  ​concave downward on   
B)  ​concave downward on   ; concave upward on   
C)  ​concave upward on   ; concave downward on   
D)  ​​concave downward on   ; ​concave upward on   
E)  ​concave upward on   ; concave downward on

Question 7

​Find the derivative of

Accepted Answer

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

Question 8

A small business purchases a piece of equipment for $1,740.After 5 years,the equipment will be outdated,having no value.Write a linear equation giving the value V of the equipment in terms of time t in years,   ​

Accepted Answer

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

Question 9

​Find   implicitly for   ​

Accepted Answer

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

Question 10

Match the function   with one of the following graphs. ​

Accepted Answer

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

Question 11

Find the third derivative. ​   ​

Accepted Answer

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

Question 12

​For the given function,find the critical numbers. ​
​   ​

Accepted Answer

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

Question 13

Find the exponential function   that passes through the two given points (0,7)and (6,8).

Accepted Answer

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

Question 14

Determine the continuity of the function below. ​   ​​

Accepted Answer

A)  ​discontinuous at   
B)  ​continuous on the entire real number line 
C)  ​discontinuous at   
D)  ​discontinuous at   
E)  ​discontinuous at   
A)  ​discontinuous at   
B)  ​continuous on the entire real number line 
C)  ​discontinuous at   
D)  ​discontinuous at   
E)  ​discontinuous at

Question 15

​Suppose the resident population P(in millions)of the United States can be modeled by   ,   ,where   corresponds to 1800.Analytically find the minimum and maximum populations in the U.S.for   ​

Accepted Answer

A)  ​The population is minimum at   and maximum at   
B)  ​​The population is minimum at   and maximum at   
C)  ​​​The population is minimum at   and maximum at   
D)  ​​The population is minimum at   and maximum at   
E)  ​The population is minimum at   and maximum at   
A)  ​The population is minimum at   and maximum at   
B)  ​​The population is minimum at   and maximum at   
C)  ​​​The population is minimum at   and maximum at   
D)  ​​The population is minimum at   and maximum at   
E)  ​The population is minimum at   and maximum at

Question 16

​If   ,find   ​

Accepted Answer

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

Question 17

The number of people who donated to a certain organization between 1975 and 1992 can be modeled by the equation   donors,where t is the number of years after 1975.Find the inflection point(s)from   through   ,if any exist. ​

Accepted Answer

A)  There are no inflection points from   
B)  There is one inflection point at   
C)  There are inflection points at   
D)  There is one inflection point at   
E)  There are inflection points at   ,   ,   
A)  There are no inflection points from   
B)  There is one inflection point at   
C)  There are inflection points at   
D)  There is one inflection point at   
E)  There are inflection points at   ,   ,

Question 18

​Find the speed v,in miles per hour,that will minimize costs on a 125-mile delivery trip.The cost per hour for fuel is   dollars,and the driver is paid   dollars per hour.(Assume there are no costs other than wages and fuel.) ​

Accepted Answer

A)  ​75 mph 
B)  ​125 mph 
C)  ​200 mph 
D)  80​ mph 
E)  ​40 mph 
A)  ​75 mph 
B)  ​125 mph 
C)  ​200 mph 
D)  80​ mph 
E)  ​40 mph

Question 19

​Find any horizontal asymptotes for the given function. ​
​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​no horizontal asymptotes 
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​no horizontal asymptotes

Question 20

​A deposit of $8,500 is made in an account that pays 6% compounded every 7 months.The amount A in the account after t years is   ,   What are the points of discontinuity of graph of   ? (Here,the brackets indicate the greatest integer function.) ​

Accepted Answer

A)  ​1 ,   ,   ,   ,... 
B)  ​0 , 1 , 2 ,... 
C)  ​7 , 14 , 21 ,.... 
D)  ​1 , 2 , 3 ,... 
E)  ​   ,   ,   ,... 
A)  ​1 ,   ,   ,   ,... 
B)  ​0 , 1 , 2 ,... 
C)  ​7 , 14 , 21 ,.... 
D)  ​1 , 2 , 3 ,... 
E)  ​   ,   ,   ,...

Find an equation of the line that passes through the point and has the slope m that is undefined.

Find the x-value at which the given function has a point of inflection.

Volume.A rectangular box with a square base is to be formed from a square piece of metal with 54-inch sides.If a square piece with side x is cut from each corner of the metal and the sides are folded up to form an open box,the volume of the box is What value of x will maximize the volume of the box?

Find

If the total cost function for a product is dollars.Find the minimum average cost.

Determine the open intervals on which the graph of is concave downward or concave upward.

Find the derivative of

A small business purchases a piece of equipment for $1,740.After 5 years,the equipment will be outdated,having no value.Write a linear equation giving the value V of the equipment in terms of time t in years,

Find implicitly for

Match the function with one of the following graphs.

Find the third derivative.

For the given function,find the critical numbers.

Find the exponential function that passes through the two given points (0,7)and (6,8).

Determine the continuity of the function below.

Suppose the resident population P(in millions)of the United States can be modeled by , ,where corresponds to 1800.Analytically find the minimum and maximum populations in the U.S.for

If ,find

The number of people who donated to a certain organization between 1975 and 1992 can be modeled by the equation donors,where t is the number of years after 1975.Find the inflection point(s)from through ,if any exist.

Find the speed v,in miles per hour,that will minimize costs on a 125-mile delivery trip.The cost per hour for fuel is dollars,and the driver is paid dollars per hour.(Assume there are no costs other than wages and fuel.)

Find any horizontal asymptotes for the given function.

A deposit of $8,500 is made in an account that pays 6% compounded every 7 months.The amount A in the account after t years is , What are the points of discontinuity of graph of ? (Here,the brackets indicate the greatest integer function.)

Differentiation

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 1: Functions, graphs, and Limits

​Find an equation of the line that passes through the point and has the slope m that is undefined. ​

​Find the x-value at which the given function has a point of inflection. ​ ​ ​

​Find ​

​If the total cost function for a product is dollars.Find the minimum average cost. ​

​Determine the open intervals on which the graph of is concave downward or concave upward. ​

​Find the derivative of

A small business purchases a piece of equipment for $1,740.After 5 years,the equipment will be outdated,having no value.Write a linear equation giving the value V of the equipment in terms of time t in years, ​

​Find implicitly for ​

Match the function with one of the following graphs. ​

Find the third derivative. ​ ​

​For the given function,find the critical numbers. ​ ​ ​

Find the exponential function that passes through the two given points (0,7)and (6,8).

Determine the continuity of the function below. ​ ​​

​Suppose the resident population P(in millions)of the United States can be modeled by , ,where corresponds to 1800.Analytically find the minimum and maximum populations in the U.S.for ​

​If ,find ​

The number of people who donated to a certain organization between 1975 and 1992 can be modeled by the equation donors,where t is the number of years after 1975.Find the inflection point(s)from through ,if any exist. ​

​Find the speed v,in miles per hour,that will minimize costs on a 125-mile delivery trip.The cost per hour for fuel is dollars,and the driver is paid dollars per hour.(Assume there are no costs other than wages and fuel.) ​

​Find any horizontal asymptotes for the given function. ​ ​ ​

​A deposit of $8,500 is made in an account that pays 6% compounded every 7 months.The amount A in the account after t years is , What are the points of discontinuity of graph of ? (Here,the brackets indicate the greatest integer function.) ​

Differentiation

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 an equation of the line that passes through the point and has the slope m that is undefined.

Find the x-value at which the given function has a point of inflection.

Find

If the total cost function for a product is dollars.Find the minimum average cost.

Determine the open intervals on which the graph of is concave downward or concave upward.

Find the derivative of

A small business purchases a piece of equipment for $1,740.After 5 years,the equipment will be outdated,having no value.Write a linear equation giving the value V of the equipment in terms of time t in years,

Find implicitly for

Match the function with one of the following graphs.

Find the third derivative.

For the given function,find the critical numbers.

Determine the continuity of the function below.

Suppose the resident population P(in millions)of the United States can be modeled by , ,where corresponds to 1800.Analytically find the minimum and maximum populations in the U.S.for

If ,find

The number of people who donated to a certain organization between 1975 and 1992 can be modeled by the equation donors,where t is the number of years after 1975.Find the inflection point(s)from through ,if any exist.

Find the speed v,in miles per hour,that will minimize costs on a 125-mile delivery trip.The cost per hour for fuel is dollars,and the driver is paid dollars per hour.(Assume there are no costs other than wages and fuel.)

Find any horizontal asymptotes for the given function.

A deposit of $8,500 is made in an account that pays 6% compounded every 7 months.The amount A in the account after t years is , What are the points of discontinuity of graph of ? (Here,the brackets indicate the greatest integer function.)