Question 1

Find the derivative of the following function. ​

Accepted Answer

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

Question 2

Suppose that the demand for a product is given by   . Find the elasticity when   and   and also determine how would revenue be affected by a price increase? ​

Accepted Answer

A)   
) A price increase will decrease the total revenue. 
B)   
) A price increase will decrease the total revenue. 
C)   
) A price increase will increase the total revenue. 
D)   
) A price increase will increase the total revenue. 
E)   
) A price increase will decrease the total revenue. 
A)   
) A price increase will decrease the total revenue. 
B)   
) A price increase will decrease the total revenue. 
C)   
) A price increase will increase the total revenue. 
D)   
) A price increase will increase the total revenue. 
E)   
) A price increase will decrease the total revenue.

Question 3

Find the relative maxima, and use a graphing utility to check your results. ​Round your answer to two decimal places. ​   ​

Accepted Answer

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

Question 4

Suppose the concentration C(t), in mg/ml, of a drug in the bloodstream t minutes after an injection is given by   Find the maximum concentration and when it occurs. ​

Accepted Answer

A) Maximum concentration of 14.72 mg/ml occurs after 2.00 minutes. 
B) Maximum concentration of 7.79 mg/ml occurs after 0.50 minutes. 
C) Maximum concentration of 1.35 mg/ml occurs after 10.00minutes. 
D) Maximum concentration of 14.46 mg/ml occurs after 2.40 minutes. 
E) Maximum concentration of 13.81 mg/ml occurs after 2.80 minutes. 
A) Maximum concentration of 14.72 mg/ml occurs after 2.00 minutes. 
B) Maximum concentration of 7.79 mg/ml occurs after 0.50 minutes. 
C) Maximum concentration of 1.35 mg/ml occurs after 10.00minutes. 
D) Maximum concentration of 14.46 mg/ml occurs after 2.40 minutes. 
E) Maximum concentration of 13.81 mg/ml occurs after 2.80 minutes.

Question 5

Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the radius of the tumor to decrease at a rate of 9 millimeters per month. At what rate is the surface area of the tumor decreasing when the radius is 2 mm? ​

Accepted Answer

A) Surface area is decreasing at the rate of 288π mm2/month. 
B) Surface area is decreasing at the rate of 72π mm2/month. 
C) Surface area is decreasing at the rate of 32π mm2/month. 
D) Surface area is decreasing at the rate of 16π mm2/month. 
E) Surface area is decreasing at the rate of 144π mm2/month. 
A) Surface area is decreasing at the rate of 288π mm2/month. 
B) Surface area is decreasing at the rate of 72π mm2/month. 
C) Surface area is decreasing at the rate of 32π mm2/month. 
D) Surface area is decreasing at the rate of 16π mm2/month. 
E) Surface area is decreasing at the rate of 144π mm2/month.

Question 6

Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 7

Find dp/dq for the following equation: ​   .
​

Accepted Answer

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

Question 8

Between the years 1960 and 2002, the percent of women in the work force can be modeled by   , where x is the number of years past 1950 (Source: U.S. Bureau of Labor Statistics). If this model is accurate beyond 2002, at what rate will the percent be changing in 2017? ​

Accepted Answer

A) In 2017, the rate will be changing at 0.270% per year. 
B) In 2017, the rate will be changing at 0.405% per year. 
C) In 2017, the rate will be changing at 0.007% per year. 
D) In 2017, the rate will be changing at 0.971% per year. 
E) In 2017, the rate will be changing at 0.217% per year. 
A) In 2017, the rate will be changing at 0.270% per year. 
B) In 2017, the rate will be changing at 0.405% per year. 
C) In 2017, the rate will be changing at 0.007% per year. 
D) In 2017, the rate will be changing at 0.971% per year. 
E) In 2017, the rate will be changing at 0.217% per year.

Question 9

Find   . ​   ​

Accepted Answer

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

Question 10

Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 11

If   , find   . ​

Accepted Answer

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

Question 12

Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 13

p is the price per unit in dollars and q is the number of units. If the daily demand for a product is given by the function   and the daily supply before taxation is   , find the tax per item that maximizes tax revenue. Round your answer to the nearest cent.

Accepted Answer

A) $714.19 per item 
B) $574.72 per item 
C) $853.66 per item 
D) $622.04 per item 
E) $503.73 per item 
A) $714.19 per item 
B) $574.72 per item 
C) $853.66 per item 
D) $622.04 per item 
E) $503.73 per item

Question 14

p is the price per unit in dollars and q is the number of units. If the demand and supply functions for a product are   , and   , respectively, how many items will maximize the tax revenue? ​

Accepted Answer

A) 730 
B) 610 
C) 665 
D) 647 
E) 70 
A) 730 
B) 610 
C) 665 
D) 647 
E) 70

Question 15

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) 7.52 
B) 3.35 
C) 2.74 
D) 4.26 
E) 37.33 
A) 7.52 
B) 3.35 
C) 2.74 
D) 4.26 
E) 37.33

Question 16

Find the maximum value of y. Use a graphing utility to verify your conclusion. Round your answer to three decimal places. ​   ​

Accepted Answer

A) 2.828 
B) 6.600 
C) 0.157 
D) 0.889 
E) 0.943 
A) 2.828 
B) 6.600 
C) 0.157 
D) 0.889 
E) 0.943

Question 17

Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 18

Assume that water is being purified by causing it to flow through a conical filter that has a height of 5 inches and a radius of 4 inches. If the depth of the water is decreasing at a rate of 3 inches per minute when the depth is 4 inches, at what rate is the volume of water flowing out of the filter at this instant? Round your answer to two decimal places. ​

Accepted Answer

A) The water is flowing out at the approximate rate of 96.51 in3 per minute. 
B) The water is flowing out at the approximate rate of 289.53 in3 per minute. 
C) The water is flowing out at the approximate rate of 74.39 in3 per minute. 
D) The water is flowing out at the approximate rate of 52.28 in3 per minute. 
E) The water is flowing out at the approximate rate of 70.62 in3 per minute. 
A) The water is flowing out at the approximate rate of 96.51 in3 per minute. 
B) The water is flowing out at the approximate rate of 289.53 in3 per minute. 
C) The water is flowing out at the approximate rate of 74.39 in3 per minute. 
D) The water is flowing out at the approximate rate of 52.28 in3 per minute. 
E) The water is flowing out at the approximate rate of 70.62 in3 per minute.

Question 19

If the demand function for q units of a commodity at p$ per unit is given by   , find the rate of change of quantity with respect to price when   . Round your answer to three decimal places.

Accepted Answer

A) 0.017 
B) -0.017 
C) 0.009 
D) -0.011 
E) 0.005 
A) 0.017 
B) -0.017 
C) 0.009 
D) -0.011 
E) 0.005

Question 20

Find the derivative of the following function. ​   ​

Accepted Answer

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

Find the derivative of the following function.

Suppose that the demand for a product is given by . Find the elasticity when and and also determine how would revenue be affected by a price increase?

Find the relative maxima, and use a graphing utility to check your results. Round your answer to two decimal places.

Suppose the concentration C(t), in mg/ml, of a drug in the bloodstream t minutes after an injection is given by Find the maximum concentration and when it occurs.

Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the radius of the tumor to decrease at a rate of 9 millimeters per month. At what rate is the surface area of the tumor decreasing when the radius is 2 mm?

Find the derivative of the following function.

Find dp/dq for the following equation: .

Between the years 1960 and 2002, the percent of women in the work force can be modeled by , where x is the number of years past 1950 (Source: U.S. Bureau of Labor Statistics). If this model is accurate beyond 2002, at what rate will the percent be changing in 2017?

Find .

Find the derivative of the following function.

If , find .

Find the derivative of the following function.

p is the price per unit in dollars and q is the number of units. If the daily demand for a product is given by the function and the daily supply before taxation is , find the tax per item that maximizes tax revenue. Round your answer to the nearest cent.

p is the price per unit in dollars and q is the number of units. If the demand and supply functions for a product are , and , respectively, how many items will maximize the tax revenue?

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.

Find the maximum value of y. Use a graphing utility to verify your conclusion. Round your answer to three decimal places.

Find the derivative of the following function.

If the demand function for q units of a commodity at p$ per unit is given by , find the rate of change of quantity with respect to price when . Round your answer to three decimal places.

Find the derivative of the following function.

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 the derivative of the following function. ​

Suppose that the demand for a product is given by . Find the elasticity when and and also determine how would revenue be affected by a price increase? ​

Find the relative maxima, and use a graphing utility to check your results. ​Round your answer to two decimal places. ​ ​

Suppose the concentration C(t), in mg/ml, of a drug in the bloodstream t minutes after an injection is given by Find the maximum concentration and when it occurs. ​

Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the radius of the tumor to decrease at a rate of 9 millimeters per month. At what rate is the surface area of the tumor decreasing when the radius is 2 mm? ​

Find the derivative of the following function. ​ ​

Find dp/dq for the following equation: ​ . ​

Between the years 1960 and 2002, the percent of women in the work force can be modeled by , where x is the number of years past 1950 (Source: U.S. Bureau of Labor Statistics). If this model is accurate beyond 2002, at what rate will the percent be changing in 2017? ​

Find . ​ ​

Find the derivative of the following function. ​ ​

If , find . ​

Find the derivative of the following function. ​ ​

p is the price per unit in dollars and q is the number of units. If the daily demand for a product is given by the function and the daily supply before taxation is , find the tax per item that maximizes tax revenue. Round your answer to the nearest cent.

p is the price per unit in dollars and q is the number of units. If the demand and supply functions for a product are , and , respectively, how many items will maximize the tax revenue? ​

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. ​

Find the maximum value of y. Use a graphing utility to verify your conclusion. Round your answer to three decimal places. ​ ​

Find the derivative of the following function. ​ ​

If the demand function for q units of a commodity at p$ per unit is given by , find the rate of change of quantity with respect to price when . Round your answer to three decimal places.

Find the derivative of the following function. ​ ​

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 the derivative of the following function.

Suppose that the demand for a product is given by . Find the elasticity when and and also determine how would revenue be affected by a price increase?

Find the relative maxima, and use a graphing utility to check your results. Round your answer to two decimal places.

Suppose the concentration C(t), in mg/ml, of a drug in the bloodstream t minutes after an injection is given by Find the maximum concentration and when it occurs.

Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the radius of the tumor to decrease at a rate of 9 millimeters per month. At what rate is the surface area of the tumor decreasing when the radius is 2 mm?

Find the derivative of the following function.

Find dp/dq for the following equation: .

Between the years 1960 and 2002, the percent of women in the work force can be modeled by , where x is the number of years past 1950 (Source: U.S. Bureau of Labor Statistics). If this model is accurate beyond 2002, at what rate will the percent be changing in 2017?

Find .

Find the derivative of the following function.

If , find .

Find the derivative of the following function.

p is the price per unit in dollars and q is the number of units. If the demand and supply functions for a product are , and , respectively, how many items will maximize the tax revenue?

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.

Find the maximum value of y. Use a graphing utility to verify your conclusion. Round your answer to three decimal places.

Find the derivative of the following function.

Find the derivative of the following function.