Question 1

Find   if   ​

Accepted Answer

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

Question 2

p is in dollars and q is the number of units. Find the elasticity of the demand function   at   . Round your answer to two decimal places.

Accepted Answer

A) 3.07 
B) 0.33 
C) -0.33 
D) 1.00 
E) -1.00 
A) 3.07 
B) 0.33 
C) -0.33 
D) 1.00 
E) -1.00

Question 3

Suppose the weekly demand function is   and the supply function before taxation is   , determine what tax per item will maximize the total tax revenue? ​

Accepted Answer

A) $465/item 
B) $205/item 
C) $115/item 
D) $163/item 
E) $128/item 
A) $465/item 
B) $205/item 
C) $115/item 
D) $163/item 
E) $128/item

Question 4

Suppose that the price p (in dollars) of a product is given by the demand function   where x represents the quantity demanded. If the daily demand is increase at a rate of 5 units per day, at what rate is the price changing when the demand is 64 units? Round your answer to two decimal places. ​

Accepted Answer

A) The price is decreasing at approximately 0.24 dollars per day. 
B) The price is decreasing at approximately 0.04 dollars per day. 
C) The price is decreasing at approximately 0.14 dollars per day. 
D) The price is decreasing at approximately 0.03 dollars per day. 
E) The price is decreasing at approximately 0.08 dollars per day. 
A) The price is decreasing at approximately 0.24 dollars per day. 
B) The price is decreasing at approximately 0.04 dollars per day. 
C) The price is decreasing at approximately 0.14 dollars per day. 
D) The price is decreasing at approximately 0.03 dollars per day. 
E) The price is decreasing at approximately 0.08 dollars per day.

Question 5

Find   for the following equation: ​   ​

Accepted Answer

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

Question 6

p is the price per unit in dollars and q is the number of units. The monthly demand function is   and the supply function before taxation is   . Find what tax per item will maximize the total revenue and use this to find the maximum tax revenue. ​

Accepted Answer

A) $3,780 
B) $840 
C) $3,360 
D) $2,160 
E) $2,820 
A) $3,780 
B) $840 
C) $3,360 
D) $2,160 
E) $2,820

Question 7

Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 8

Write the equation of the line tangent to the graph of   at   . ​

Accepted Answer

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

Question 9

Find   ​   ​

Accepted Answer

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

Question 10

The resistance R of a blood vessel to the flow of blood is a function of the radius r of the blood vessel and is given by   , where k is a constant. For   find the percent rate of change of the resistance of a blood vessel in terms of the percent rate of change in the radius of the blood vessel. ​

Accepted Answer

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

Question 11

Suppose the weekly demand function for a product is   where p is the price in thousands of dollars and q is the number of units demanded. What is the elasticity of demand when the price is $1,000 and the quantity demanded is 357? Round your answer to two decimal places. ​

Accepted Answer

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

Question 12

Which of the following functions has the same derivative as the function below? ​   ​

Accepted Answer

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

Question 13

Write the equation of the line tangent to the curve   at the point   . ​

Accepted Answer

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

Question 14

Find the relative minima, and use a graphing utility to check your results. ​   ​

Accepted Answer

A) ​   
B)    
C)    
D)    
E) does not exist 
A) ​   
B)    
C)    
D)    
E) does not exist

Question 15

The supply function for a product is given by   , where x is the number of units supplied and p is the price in dollars. If the price is increasing at a rate of $1 per month, at what rate is the supply changing when   Round your answer to three decimal places. ​

Accepted Answer

A) 0.013 units per month 
B) 0.299 units per month 
C) 0.043 units per month 
D) 0.066 units per month 
E) 0.033 units per month 
A) 0.013 units per month 
B) 0.299 units per month 
C) 0.043 units per month 
D) 0.066 units per month 
E) 0.033 units per month

Question 16

Total personal income in the U.S. (in billions of dollars) for selected years from 1960 to 2002 is given in the following table. ​   ​
​
These data can be modeled by   , where x is the number of years past 1960. Use the data to find the average rate of change from 2000 to 2002, which can be used to approximate the rate of change in 2002. Round your answer to the nearest ten million dollar.
​

Accepted Answer

A) $3.20 billion per year 
B) $2.83 billion per year 
C) $3.74 billion per year 
D) $3.84 billion per year 
E) $3.69 billion per year 
A) $3.20 billion per year 
B) $2.83 billion per year 
C) $3.74 billion per year 
D) $3.84 billion per year 
E) $3.69 billion per year

Question 17

Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 18

Find   . ​   ​

Accepted Answer

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

Question 19

For the given equation, find the slope of the tangent to the curve at the point   . Round your answer to two decimal places.

Accepted Answer

A) -1.50 
B) -0.67 
C) -3.81 
D) 0.00 
E) undefined 
A) -1.50 
B) -0.67 
C) -3.81 
D) 0.00 
E) undefined

Question 20

Two boats leave the same port at the same time, with boat A traveling north at 20 knots (nautical miles per hour) and boat B traveling east at 40 knots. How fast is the distance between them changing when boat A is 4 nautical miles from port? Round your answer to two decimal places. ​

Accepted Answer

A) The distance between the boats is changing at the rate of 35.78 knots. 
B) The distance between the boats is changing at the rate of 13.42 knots. 
C) The distance between the boats is changing at the rate of 44.72 knots. 
D) The distance between the boats is changing at the rate of 38.01 knots. 
E) The distance between the boats is changing at the rate of 100.00 knots. 
A) The distance between the boats is changing at the rate of 35.78 knots. 
B) The distance between the boats is changing at the rate of 13.42 knots. 
C) The distance between the boats is changing at the rate of 44.72 knots. 
D) The distance between the boats is changing at the rate of 38.01 knots. 
E) The distance between the boats is changing at the rate of 100.00 knots.

Find if

p is in dollars and q is the number of units. Find the elasticity of the demand function at . Round your answer to two decimal places.

Suppose the weekly demand function is and the supply function before taxation is , determine what tax per item will maximize the total tax revenue?

Suppose that the price p (in dollars) of a product is given by the demand function where x represents the quantity demanded. If the daily demand is increase at a rate of 5 units per day, at what rate is the price changing when the demand is 64 units? Round your answer to two decimal places.

Find for the following equation:

p is the price per unit in dollars and q is the number of units. The monthly demand function is and the supply function before taxation is . Find what tax per item will maximize the total revenue and use this to find the maximum tax revenue.

Find the derivative of the following function.

Write the equation of the line tangent to the graph of at .

Find

The resistance R of a blood vessel to the flow of blood is a function of the radius r of the blood vessel and is given by , where k is a constant. For find the percent rate of change of the resistance of a blood vessel in terms of the percent rate of change in the radius of the blood vessel.

Suppose the weekly demand function for a product is where p is the price in thousands of dollars and q is the number of units demanded. What is the elasticity of demand when the price is $1,000 and the quantity demanded is 357? Round your answer to two decimal places.

Which of the following functions has the same derivative as the function below?

Write the equation of the line tangent to the curve at the point .

Find the relative minima, and use a graphing utility to check your results.

The supply function for a product is given by , where x is the number of units supplied and p is the price in dollars. If the price is increasing at a rate of $1 per month, at what rate is the supply changing when Round your answer to three decimal places.

Find the derivative of the following function.

Find .

For the given equation, find the slope of the tangent to the curve at the point . Round your answer to two decimal places.

Two boats leave the same port at the same time, with boat A traveling north at 20 knots (nautical miles per hour) and boat B traveling east at 40 knots. How fast is the distance between them changing when boat A is 4 nautical miles from port? Round your answer to two decimal places.

Algebraic Concepts

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability; Data Description

Derivatives

Applications of Derivatives

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Exam 12: Derivatives Continued

Find if ​

p is in dollars and q is the number of units. Find the elasticity of the demand function at . Round your answer to two decimal places.

Suppose the weekly demand function is and the supply function before taxation is , determine what tax per item will maximize the total tax revenue? ​

Suppose that the price p (in dollars) of a product is given by the demand function where x represents the quantity demanded. If the daily demand is increase at a rate of 5 units per day, at what rate is the price changing when the demand is 64 units? Round your answer to two decimal places. ​

Find for the following equation: ​ ​

p is the price per unit in dollars and q is the number of units. The monthly demand function is and the supply function before taxation is . Find what tax per item will maximize the total revenue and use this to find the maximum tax revenue. ​

Find the derivative of the following function. ​ ​

Write the equation of the line tangent to the graph of at . ​

Find ​ ​

The resistance R of a blood vessel to the flow of blood is a function of the radius r of the blood vessel and is given by , where k is a constant. For find the percent rate of change of the resistance of a blood vessel in terms of the percent rate of change in the radius of the blood vessel. ​

Suppose the weekly demand function for a product is where p is the price in thousands of dollars and q is the number of units demanded. What is the elasticity of demand when the price is $1,000 and the quantity demanded is 357? Round your answer to two decimal places. ​

Which of the following functions has the same derivative as the function below? ​ ​

Write the equation of the line tangent to the curve at the point . ​

Find the relative minima, and use a graphing utility to check your results. ​ ​

The supply function for a product is given by , where x is the number of units supplied and p is the price in dollars. If the price is increasing at a rate of $1 per month, at what rate is the supply changing when Round your answer to three decimal places. ​

Find the derivative of the following function. ​ ​

Find . ​ ​

For the given equation, find the slope of the tangent to the curve at the point . Round your answer to two decimal places.

Two boats leave the same port at the same time, with boat A traveling north at 20 knots (nautical miles per hour) and boat B traveling east at 40 knots. How fast is the distance between them changing when boat A is 4 nautical miles from port? Round your answer to two decimal places. ​

Algebraic Concepts

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability; Data Description

Derivatives

Applications of Derivatives

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Find if

Suppose the weekly demand function is and the supply function before taxation is , determine what tax per item will maximize the total tax revenue?

Suppose that the price p (in dollars) of a product is given by the demand function where x represents the quantity demanded. If the daily demand is increase at a rate of 5 units per day, at what rate is the price changing when the demand is 64 units? Round your answer to two decimal places.

Find for the following equation:

p is the price per unit in dollars and q is the number of units. The monthly demand function is and the supply function before taxation is . Find what tax per item will maximize the total revenue and use this to find the maximum tax revenue.

Find the derivative of the following function.

Write the equation of the line tangent to the graph of at .

Find

The resistance R of a blood vessel to the flow of blood is a function of the radius r of the blood vessel and is given by , where k is a constant. For find the percent rate of change of the resistance of a blood vessel in terms of the percent rate of change in the radius of the blood vessel.

Suppose the weekly demand function for a product is where p is the price in thousands of dollars and q is the number of units demanded. What is the elasticity of demand when the price is $1,000 and the quantity demanded is 357? Round your answer to two decimal places.

Which of the following functions has the same derivative as the function below?

Write the equation of the line tangent to the curve at the point .

Find the relative minima, and use a graphing utility to check your results.

The supply function for a product is given by , where x is the number of units supplied and p is the price in dollars. If the price is increasing at a rate of $1 per month, at what rate is the supply changing when Round your answer to three decimal places.

Find the derivative of the following function.

Find .

Two boats leave the same port at the same time, with boat A traveling north at 20 knots (nautical miles per hour) and boat B traveling east at 40 knots. How fast is the distance between them changing when boat A is 4 nautical miles from port? Round your answer to two decimal places.