Question 1

Find any vertical asymptotes for the given function.

Accepted Answer

A)    
B)    
C)    
D)    
E) no vertical asymptotes 
A)    
B)    
C)    
D)    
E) no vertical asymptotes A

Question 2

Analytically determine the location(s) of any horizontal asymptote(s).

Accepted Answer

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

Question 3

Suppose that the oxygen level P (for purity) in a body of water t months after an oil spill is given by   . Find how long it will be before the rate of change of P is maximized. That is, find the point of diminishing returns. ​

Accepted Answer

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

Question 4

Find all relative maxima of the given function.

Accepted Answer

A)    
B)    
C)    
D)    
E) no relative maxima 
A)    
B)    
C)    
D)    
E) no relative maxima

Question 5

If the total cost function for a product is   dollars. Find the minimum average cost. Round your answer to two decimal places. ​

Accepted Answer

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

Question 6

A rectangular box with a square base is to be formed from a square piece of metal with 30-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)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 7

A function and its graph are given. Use the graph to find the vertical asymptotes, if they exist, where   . Confirm your results analytically.

Accepted Answer

A)    
B)    
C)    
D)    
E) no vertical asymptotes 
A)    
B)    
C)    
D)    
E) no vertical asymptotes

Question 8

A function and its first and second derivatives are given. Use these to find any relative maxima.

Accepted Answer

A)    
B)    
C)    
D)    
E) no relative maxima 
A)    
B)    
C)    
D)    
E) no relative maxima

Question 9

A function and its first and second derivatives are given. Use these to find any points of inflection. Round your answers to two decimal places.       ​

Accepted Answer

A)    
B)    
C)    
D)    
E) no points of inflection 
A)    
B)    
C)    
D)    
E) no points of inflection

Question 10

For the given function, find the critical values.

Accepted Answer

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

Question 11

Use the graph shown in the figure and identify points from A through I that satisfy the given condition. ​   and

Accepted Answer

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

Question 12

A kennel of 750 square feet is to be constructed as shown. The cost is $9 per running foot for the sides and $3 per running foot for the ends and dividers. What are the dimensions of the kennel that will minimize the cost? ​
​

Accepted Answer

A) The dimensions of the kennel that will minimize the cost are 25 feet for ends and dividers and 30 feet for sides. 
B) The dimensions of the kennel that will minimize the cost are 23 feet for ends and dividers and 31 feet for sides. 
C) The dimensions of the kennel that will minimize the cost are 31 feet for ends and dividers and 23 feet for sides. 
D) The dimensions of the kennel that will minimize the cost are 23 feet for ends and dividers and 30 feet for sides. 
E) The dimensions of the kennel that will minimize the cost are 30 feet for ends and dividers and 25 feet for sides. 
A) The dimensions of the kennel that will minimize the cost are 25 feet for ends and dividers and 30 feet for sides. 
B) The dimensions of the kennel that will minimize the cost are 23 feet for ends and dividers and 31 feet for sides. 
C) The dimensions of the kennel that will minimize the cost are 31 feet for ends and dividers and 23 feet for sides. 
D) The dimensions of the kennel that will minimize the cost are 23 feet for ends and dividers and 30 feet for sides. 
E) The dimensions of the kennel that will minimize the cost are 30 feet for ends and dividers and 25 feet for sides.

Question 13

For the given function, find intervals of x-values where the function is decreasing.

Accepted Answer

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

Question 14

A company handles an apartment building with 80 units. Experience has shown that if the rent for each of the units is $360 per month, all the units will be filled, but 1 unit will become vacant for each $10 increase in the monthly rate. What rent should be charged to maximize the total revenue from the building if the upper limit on the rent is $600 per month? ​

Accepted Answer

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

Question 15

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 16

A ball thrown into the air from a building 140 ft high travels along a path described by   where y is the height of the ball in feet and x is the horizontal distance of the ball from the building in feet. What is the maximum height the ball will reach? Round your answer to one decimal place. ​

Accepted Answer

A) ​180.0 feet 
B) 220.0​ feet 
C) 210.0 ​feet 
D) 195.0​ feet 
E) 200.0​ feet 
A) ​180.0 feet 
B) 220.0​ feet 
C) 210.0 ​feet 
D) 195.0​ feet 
E) 200.0​ feet

Question 17

The millions of worldwide cellular subscribers can be modeled by   where t is the number of years past 1994. In what year does the model predict the number of worldwide cellular subscribers will reach a maximum? ​

Accepted Answer

A) year 2016 
B) year 2013 
C) year 2017 
D) year 2014 
E) year 2015 
A) year 2016 
B) year 2013 
C) year 2017 
D) year 2014 
E) year 2015

Question 18

A function and its first and second derivatives are given. Use these to find all relative minima.       ​

Accepted Answer

A)    
B)    
C)    
D)    
E) no relative minima 
A)    
B)    
C)    
D)    
E) no relative minima

Question 19

The percent p of impurities that can be removed from the waste water of a manufacturing process at a cost of C dollars is given by   . Find any horizontal asymptotes. ​

Accepted Answer

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

Question 20

For the given function, find all intervals of x-values where the function is increasing.

Accepted Answer

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

Find any vertical asymptotes for the given function.

Analytically determine the location(s) of any horizontal asymptote(s).

Suppose that the oxygen level P (for purity) in a body of water t months after an oil spill is given by . Find how long it will be before the rate of change of P is maximized. That is, find the point of diminishing returns.

Find all relative maxima of the given function.

If the total cost function for a product is dollars. Find the minimum average cost. Round your answer to two decimal places.

A rectangular box with a square base is to be formed from a square piece of metal with 30-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?

A function and its graph are given. Use the graph to find the vertical asymptotes, if they exist, where . Confirm your results analytically.

A function and its first and second derivatives are given. Use these to find any relative maxima.

A function and its first and second derivatives are given. Use these to find any points of inflection. Round your answers to two decimal places.

For the given function, find the critical values.

Use the graph shown in the figure and identify points from A through I that satisfy the given condition. and

A kennel of 750 square feet is to be constructed as shown. The cost is $9 per running foot for the sides and $3 per running foot for the ends and dividers. What are the dimensions of the kennel that will minimize the cost?

For the given function, find intervals of x-values where the function is decreasing.

Find any horizontal asymptotes for the given function.

A ball thrown into the air from a building 140 ft high travels along a path described by where y is the height of the ball in feet and x is the horizontal distance of the ball from the building in feet. What is the maximum height the ball will reach? Round your answer to one decimal place.

The millions of worldwide cellular subscribers can be modeled by where t is the number of years past 1994. In what year does the model predict the number of worldwide cellular subscribers will reach a maximum?

A function and its first and second derivatives are given. Use these to find all relative minima.

The percent p of impurities that can be removed from the waste water of a manufacturing process at a cost of C dollars is given by . Find any horizontal asymptotes.

For the given function, find all intervals of x-values where the function is increasing.

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

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Exam 11: Applications of Derivatives

Find any vertical asymptotes for the given function.

Analytically determine the location(s) of any horizontal asymptote(s).

Suppose that the oxygen level P (for purity) in a body of water t months after an oil spill is given by . Find how long it will be before the rate of change of P is maximized. That is, find the point of diminishing returns. ​

Find all relative maxima of the given function.

If the total cost function for a product is dollars. Find the minimum average cost. Round your answer to two decimal places. ​

A function and its graph are given. Use the graph to find the vertical asymptotes, if they exist, where . Confirm your results analytically.

A function and its first and second derivatives are given. Use these to find any relative maxima.

A function and its first and second derivatives are given. Use these to find any points of inflection. Round your answers to two decimal places. ​

For the given function, find the critical values.

Use the graph shown in the figure and identify points from A through I that satisfy the given condition. ​ and

A kennel of 750 square feet is to be constructed as shown. The cost is $9 per running foot for the sides and $3 per running foot for the ends and dividers. What are the dimensions of the kennel that will minimize the cost? ​ ​

For the given function, find intervals of x-values where the function is decreasing.

Find any horizontal asymptotes for the given function.

A ball thrown into the air from a building 140 ft high travels along a path described by where y is the height of the ball in feet and x is the horizontal distance of the ball from the building in feet. What is the maximum height the ball will reach? Round your answer to one decimal place. ​

The millions of worldwide cellular subscribers can be modeled by where t is the number of years past 1994. In what year does the model predict the number of worldwide cellular subscribers will reach a maximum? ​

A function and its first and second derivatives are given. Use these to find all relative minima. ​

The percent p of impurities that can be removed from the waste water of a manufacturing process at a cost of C dollars is given by . Find any horizontal asymptotes. ​

For the given function, find all intervals of x-values where the function is increasing.

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

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Suppose that the oxygen level P (for purity) in a body of water t months after an oil spill is given by . Find how long it will be before the rate of change of P is maximized. That is, find the point of diminishing returns.

If the total cost function for a product is dollars. Find the minimum average cost. Round your answer to two decimal places.

A function and its first and second derivatives are given. Use these to find any points of inflection. Round your answers to two decimal places.

Use the graph shown in the figure and identify points from A through I that satisfy the given condition. and

A kennel of 750 square feet is to be constructed as shown. The cost is $9 per running foot for the sides and $3 per running foot for the ends and dividers. What are the dimensions of the kennel that will minimize the cost?

A ball thrown into the air from a building 140 ft high travels along a path described by where y is the height of the ball in feet and x is the horizontal distance of the ball from the building in feet. What is the maximum height the ball will reach? Round your answer to one decimal place.

The millions of worldwide cellular subscribers can be modeled by where t is the number of years past 1994. In what year does the model predict the number of worldwide cellular subscribers will reach a maximum?

A function and its first and second derivatives are given. Use these to find all relative minima.

The percent p of impurities that can be removed from the waste water of a manufacturing process at a cost of C dollars is given by . Find any horizontal asymptotes.