Question 1

​Determine the point(s),(if any),at which the graph of the function has a horizontal tangent. ​
​   ​

Accepted Answer

A)  ​0 
B)  ​0 and 3 
C)  ​0 and -3 
D)  ​3 
E)  ​There are no points at which the graph has a horizontal tangent. 
A)  ​0 
B)  ​0 and 3 
C)  ​0 and -3 
D)  ​3 
E)  ​There are no points at which the graph has a horizontal tangent.

Question 2

​Find   ​   ​

Accepted Answer

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

Question 3

​Determine the dimensions of a rectangular solid (with a square base)with maximum volume if its surface area is 441 square meters. ​

Accepted Answer

A)  ​square base side   ; height   
B)  ​square base side   ; height   
C)  ​square base side   ; height   
D)  ​​square base side   ; height   
E)  ​square base side   ; height   
A)  ​square base side   ; height   
B)  ​square base side   ; height   
C)  ​square base side   ; height   
D)  ​​square base side   ; height   
E)  ​square base side   ; height

Question 4

The variable cost for the production of a calculator is $13.75 and the initial investment is $210,000.Use differentials to approximate the change in the cost C for a one-unit increase in production when   ,where x is the number of units produced. ​

Accepted Answer

A)  ​687,500.00 dollars 
B)  ​14.75 dollars 
C)  ​688,500.00 dollars 
D)  ​13.75 dollars 
E)  ​23.75 dollars 
A)  ​687,500.00 dollars 
B)  ​14.75 dollars 
C)  ​688,500.00 dollars 
D)  ​13.75 dollars 
E)  ​23.75 dollars

Question 5

​What is the resulting balance if $4,500 is invested for 5 years at an annual rate of 7% compounded monthly?

Accepted Answer

A)  ​$4,632.79 
B)  ​$4,687.00 
C)  ​$6,075.00 
D)  ​$6,379.31 
E)  ​$8,258.80 
A)  ​$4,632.79 
B)  ​$4,687.00 
C)  ​$6,075.00 
D)  ​$6,379.31 
E)  ​$8,258.80

Question 6

​Find the extrema of the function   by analyzing its graph below. ​
​   ​

Accepted Answer

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

Question 7

​In 2004,a product has a value of $2,175.Over the next five years,its value will increase by $100 per year.Write a linear equation that gives the dollar value V in terms of the year t.(Let t = 0 represent 2000.) ​

Accepted Answer

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

Question 8

Find the limit:​ ​
​   ​

Accepted Answer

A)  ​0 
B)  ​∞ 
C)  ​1 
D)  ​-1 
E)  ​-∞ 
A)  ​0 
B)  ​∞ 
C)  ​1 
D)  ​-1 
E)  ​-∞

Question 9

​Simplify   ​

Accepted Answer

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

Question 10

​When the price of a glass of lemonade at a lemonade stand was $1.75,400 glasses were sold.When the price was lowered to $1.50,500 glasses were sold.Assume that the demand function is linear and that the marginal and fixed costs are $0.10 and $25,respectively.Find the profit P as a function of x,the number of glasses of lemonade sold. ​

Accepted Answer

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

Question 11

​Find the derivative of the function. ​   ​

Accepted Answer

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

Question 12

Find   of   ,   ​

Accepted Answer

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

Question 13

​Profit.Suppose that the monthly revenue and cost (in dollars)for x units of a product are   and   At what rate per month is the profit changing if the number of units produced and sold is 100 and is increasing at a rate of 10 units per month? ​

Accepted Answer

A)  ​11,960 per month 
B)  ​1,160 per month 
C)  ​1,960 per month 
D)  760​ per month 
E)  19,960​ per month 
A)  ​11,960 per month 
B)  ​1,160 per month 
C)  ​1,960 per month 
D)  760​ per month 
E)  19,960​ per month

Question 14

​Use the graph f ' to sketch the graph of ​f​. ​   ​

Accepted Answer

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

Question 15

Find x such that the distance between the points   and   is 5. ​

Accepted Answer

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

Question 16

​The graph of f is shown.Graph f,f ' and f '' on the same set of coordinate axes. ​
​   ​

Accepted Answer

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

Question 17

​Find   if   ​

Accepted Answer

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

Question 18

​Suppose the resident population of South Carolina (in thousands)was 4,030 in 2000 and 4,256 in 2006.Assume that the relationship between the population y and the year t is linear.Let   represent 2000.Estimate the population in 2004 by using linear model for the given data.Round your answer to the nearest thousand residents. ​

Accepted Answer

A)  ​4,482 thousand residents 
B)  ​3,879 thousand residents 
C)  ​4,105 thousand residents 
D)  ​4,181 thousand residents 
E)  ​4,407 thousand residents 
A)  ​4,482 thousand residents 
B)  ​3,879 thousand residents 
C)  ​4,105 thousand residents 
D)  ​4,181 thousand residents 
E)  ​4,407 thousand residents

Question 19

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

Accepted Answer

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

Question 20

How much more interest will be earned if $7,000 is invested for 9 years at an annual rate of 9% compounded continuously,instead of at 9% compounded quarterly? Round your answer to the nearest cent.

Accepted Answer

A)  $47.49 
B)  $93.15 
C)  $140.64 
D)  $2,924.71 
E)  $3,017.87 
A)  $47.49 
B)  $93.15 
C)  $140.64 
D)  $2,924.71 
E)  $3,017.87

Determine the point(s),(if any),at which the graph of the function has a horizontal tangent.

Find

Determine the dimensions of a rectangular solid (with a square base)with maximum volume if its surface area is 441 square meters.

The variable cost for the production of a calculator is $13.75 and the initial investment is $210,000.Use differentials to approximate the change in the cost C for a one-unit increase in production when ,where x is the number of units produced.

What is the resulting balance if $4,500 is invested for 5 years at an annual rate of 7% compounded monthly?

Find the extrema of the function by analyzing its graph below.

In 2004,a product has a value of $2,175.Over the next five years,its value will increase by $100 per year.Write a linear equation that gives the dollar value V in terms of the year t.(Let t = 0 represent 2000.)

Find the limit:

Simplify

Find the derivative of the function.

Find of ,

Profit.Suppose that the monthly revenue and cost (in dollars)for x units of a product are and At what rate per month is the profit changing if the number of units produced and sold is 100 and is increasing at a rate of 10 units per month?

Use the graph f ' to sketch the graph of f.

Find x such that the distance between the points and is 5.

The graph of f is shown.Graph f,f ' and f '' on the same set of coordinate axes.

Find if

For the given function,find all critical numbers.

How much more interest will be earned if $7,000 is invested for 9 years at an annual rate of 9% compounded continuously,instead of at 9% compounded quarterly? Round your answer to the nearest cent.

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

​Determine the point(s),(if any),at which the graph of the function has a horizontal tangent. ​ ​ ​

​Find ​ ​

​Determine the dimensions of a rectangular solid (with a square base)with maximum volume if its surface area is 441 square meters. ​

The variable cost for the production of a calculator is $13.75 and the initial investment is $210,000.Use differentials to approximate the change in the cost C for a one-unit increase in production when ,where x is the number of units produced. ​

​What is the resulting balance if $4,500 is invested for 5 years at an annual rate of 7% compounded monthly?

​Find the extrema of the function by analyzing its graph below. ​ ​ ​

​In 2004,a product has a value of $2,175.Over the next five years,its value will increase by $100 per year.Write a linear equation that gives the dollar value V in terms of the year t.(Let t = 0 represent 2000.) ​

Find the limit:​ ​ ​ ​

​Simplify ​

​Find the derivative of the function. ​ ​

Find of , ​

​Profit.Suppose that the monthly revenue and cost (in dollars)for x units of a product are and At what rate per month is the profit changing if the number of units produced and sold is 100 and is increasing at a rate of 10 units per month? ​

​Use the graph f ' to sketch the graph of ​f​. ​ ​

Find x such that the distance between the points and is 5. ​

​The graph of f is shown.Graph f,f ' and f '' on the same set of coordinate axes. ​ ​ ​

​Find if ​

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

How much more interest will be earned if $7,000 is invested for 9 years at an annual rate of 9% compounded continuously,instead of at 9% compounded quarterly? Round your answer to the nearest cent.

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

Determine the point(s),(if any),at which the graph of the function has a horizontal tangent.

Find

Determine the dimensions of a rectangular solid (with a square base)with maximum volume if its surface area is 441 square meters.

The variable cost for the production of a calculator is $13.75 and the initial investment is $210,000.Use differentials to approximate the change in the cost C for a one-unit increase in production when ,where x is the number of units produced.

What is the resulting balance if $4,500 is invested for 5 years at an annual rate of 7% compounded monthly?

Find the extrema of the function by analyzing its graph below.

In 2004,a product has a value of $2,175.Over the next five years,its value will increase by $100 per year.Write a linear equation that gives the dollar value V in terms of the year t.(Let t = 0 represent 2000.)

Find the limit:

Simplify

Find the derivative of the function.

Find of ,

Profit.Suppose that the monthly revenue and cost (in dollars)for x units of a product are and At what rate per month is the profit changing if the number of units produced and sold is 100 and is increasing at a rate of 10 units per month?

Use the graph f ' to sketch the graph of f.

Find x such that the distance between the points and is 5.

The graph of f is shown.Graph f,f ' and f '' on the same set of coordinate axes.

Find if

For the given function,find all critical numbers.