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.

Question 2

​Find  ​  ​

Accepted Answer

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

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

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

Question 6

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

Accepted Answer

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)  ​

Question 8

Find the limit:​ ​
​  ​

Accepted Answer

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

Question 9

​Simplify  ​

Accepted Answer

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)  ​

Question 11

​Find the derivative of the function. ​  ​

Accepted Answer

A)  ​  
B)  ​  
C)  ​  
D)  ​  
E)  ​

Question 12

Find  of  ,  ​

Accepted Answer

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

Question 14

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

Accepted Answer

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)

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

Question 17

​Find  if  ​

Accepted Answer

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

Question 19

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

Accepted Answer

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

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.

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.

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.