Question 1

The graph of f is shown below.For which values of x is   zero? ​   ​

Accepted Answer

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

Question 2

Find the points of inflection and discuss the concavity of the function   on the interval   . ​

Accepted Answer

A) concave down on   ;no points of inflection 
B) concave upward on   ;concave downward on
  ;inflection points at
  and
  
C) concave downward on   ;concave upward on
  ;inflection points at
  and
  
D) concave up on   ;no points of inflection 
E) none of the above 
A) concave down on   ;no points of inflection 
B) concave upward on   ;concave downward on
  ;inflection points at
  and
  
C) concave downward on   ;concave upward on
  ;inflection points at
  and
  
D) concave up on   ;no points of inflection 
E) none of the above B

Question 3

The resistance R of a certain type of resistor is   where R is measured in ohms and the temperature T is measured in degrees Celsius.Use a computer algebra system to find   . ​

Accepted Answer

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

Question 4

The ordering and transportation cost C for components used in a manufacturing process is approximated by   ,where C is measured in thousands of dollars and x is the order size in hundreds.According to Rolle's Theorem,the rate of change of the cost must be 0 for some order size in the interval   .Find this order size.Round your answer to three decimal places. ​

Accepted Answer

A) 8.196 components 
B) 5.598 components 
C) 6.674 components 
D) 5.174 components 
E) 4.098 components 
A) 8.196 components 
B) 5.598 components 
C) 6.674 components 
D) 5.174 components 
E) 4.098 components

Question 5

​Given the following conditions for   ,which graph best illustrates   ? ​   : The domain of the function is the real numbers,but   ;
​   ;   ;   .
​   for all x where   ,and   does not exist at   .   for   ,   for   ,and   does not exist at   .
​

Accepted Answer

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

Question 6

A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window (see figure).Find the dimensions of a Norman window of maximum area if the total perimeter is 38 feet. ​   ​

Accepted Answer

A)    feet;   feet 
B)    feet;   feet 
C)    feet;   feet 
D)    feet;   feet 
E)    feet;   feet 
A)    feet;   feet 
B)    feet;   feet 
C)    feet;   feet 
D)    feet;   feet 
E)    feet;   feet

Question 7

Find the value of the derivative (if it exists)of   at the indicated extremum. ​   ​

Accepted Answer

A)    is undefined. 
B)    
C)    
D)    
E)    
A)    is undefined. 
B)    
C)    
D)    
E)

Question 8

Find all points of inflection of the graph of the function   on the interval   .Round your answer to three decimal places wherever applicable. ​

Accepted Answer

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

Question 9

A rectangle is bounded by the x- and y-axes and the graph of   (see figure).What length and width should the rectangle have so that its area is a maximum? ​   ​

Accepted Answer

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

Question 10

Use differentials to approximate the value of   .Round your answer to four decimal places. ​

Accepted Answer

A) 1.8650 
B) 1.8750 
C) 1.9050 
D) 1.8850 
E) 1.8950 
A) 1.8650 
B) 1.8750 
C) 1.9050 
D) 1.8850 
E) 1.8950

Question 11

Compare   and   for   at   with   Give your answers to four decimal places. ​

Accepted Answer

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

Question 12

​For the function   ,how many of the inflection points of the function are also extrema? ​

Accepted Answer

A) ​3 
B) ​2 
C) ​1 
D) ​None 
A) ​3 
B) ​2 
C) ​1 
D) ​None

Question 13

Find all points of inflection,if any exist,of the graph of the function   .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 14

On a given day,the flow rate F (cars per hour)on a congested roadway is given by   ,where v is the speed of the traffic in miles per hour.What speed will maximize the flow rate on the road? Round your answer to the nearest mile per hour. ​

Accepted Answer

A) 19 miles per hour 
B) 17 miles per hour 
C) 18 miles per hour 
D) 10 miles per hour 
E) 20 miles per hour 
A) 19 miles per hour 
B) 17 miles per hour 
C) 18 miles per hour 
D) 10 miles per hour 
E) 20 miles per hour

Question 15

Analyze and sketch a graph of the function   . ​

Accepted Answer

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

Question 16

Find the point on the graph of the function   that is closest to the point   . ​

Accepted Answer

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

Question 17

Analyze the graph of the function   .Determine any intercepts,relative extrema,points of inflection and asymptotes.Also determine where the graph is increasing or decreasing and concave up or concave down.Then identify the graph from the choices below. ​

Accepted Answer

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

Question 18

Find all relative extrema of the function   .Use the Second Derivative Test where applicable. ​

Accepted Answer

A) relative max:   ;no relative min 
B) no relative max;no relative min 
C) relative max:   ;relative min:
  
D) relative max:   ;no relative min 
E) relative min:   ;relative max:
  
A) relative max:   ;no relative min 
B) no relative max;no relative min 
C) relative max:   ;relative min:
  
D) relative max:   ;no relative min 
E) relative min:   ;relative max:

Question 19

The graph of a function f is is shown below.Sketch the graph of the derivative   . ​   ​

Accepted Answer

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

Question 20

Sketch a graph of the function   over the interval   . ​

Accepted Answer

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

The graph of f is shown below.For which values of x is zero?

Find the points of inflection and discuss the concavity of the function on the interval .

The resistance R of a certain type of resistor is where R is measured in ohms and the temperature T is measured in degrees Celsius.Use a computer algebra system to find .

Given the following conditions for ,which graph best illustrates ? : The domain of the function is the real numbers,but ; ; ; . for all x where ,and does not exist at . for , for ,and does not exist at .

A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window (see figure).Find the dimensions of a Norman window of maximum area if the total perimeter is 38 feet.

Find the value of the derivative (if it exists)of at the indicated extremum.

Find all points of inflection of the graph of the function on the interval .Round your answer to three decimal places wherever applicable.

A rectangle is bounded by the x- and y-axes and the graph of (see figure).What length and width should the rectangle have so that its area is a maximum?

Use differentials to approximate the value of .Round your answer to four decimal places.

Compare and for at with Give your answers to four decimal places.

For the function ,how many of the inflection points of the function are also extrema?

Find all points of inflection,if any exist,of the graph of the function .Round your answers to two decimal places.

On a given day,the flow rate F (cars per hour)on a congested roadway is given by ,where v is the speed of the traffic in miles per hour.What speed will maximize the flow rate on the road? Round your answer to the nearest mile per hour.

Analyze and sketch a graph of the function .

Find the point on the graph of the function that is closest to the point .

Analyze the graph of the function .Determine any intercepts,relative extrema,points of inflection and asymptotes.Also determine where the graph is increasing or decreasing and concave up or concave down.Then identify the graph from the choices below.

Find all relative extrema of the function .Use the Second Derivative Test where applicable.

The graph of a function f is is shown below.Sketch the graph of the derivative .

Sketch a graph of the function over the interval .

Preparation for Calculus

Limits and Their Properties

Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Exam 4: Applications of Differentiation

The graph of f is shown below.For which values of x is zero? ​ ​

Find the points of inflection and discuss the concavity of the function on the interval . ​

The resistance R of a certain type of resistor is where R is measured in ohms and the temperature T is measured in degrees Celsius.Use a computer algebra system to find . ​

​Given the following conditions for ,which graph best illustrates ? ​ : The domain of the function is the real numbers,but ; ​ ; ; . ​ for all x where ,and does not exist at . for , for ,and does not exist at . ​

A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window (see figure).Find the dimensions of a Norman window of maximum area if the total perimeter is 38 feet. ​ ​

Find the value of the derivative (if it exists)of at the indicated extremum. ​ ​

Find all points of inflection of the graph of the function on the interval .Round your answer to three decimal places wherever applicable. ​

A rectangle is bounded by the x- and y-axes and the graph of (see figure).What length and width should the rectangle have so that its area is a maximum? ​ ​

Use differentials to approximate the value of .Round your answer to four decimal places. ​

Compare and for at with Give your answers to four decimal places. ​

​For the function ,how many of the inflection points of the function are also extrema? ​

Find all points of inflection,if any exist,of the graph of the function .Round your answers to two decimal places. ​

On a given day,the flow rate F (cars per hour)on a congested roadway is given by ,where v is the speed of the traffic in miles per hour.What speed will maximize the flow rate on the road? Round your answer to the nearest mile per hour. ​

Analyze and sketch a graph of the function . ​

Find the point on the graph of the function that is closest to the point . ​

Analyze the graph of the function .Determine any intercepts,relative extrema,points of inflection and asymptotes.Also determine where the graph is increasing or decreasing and concave up or concave down.Then identify the graph from the choices below. ​

Find all relative extrema of the function .Use the Second Derivative Test where applicable. ​

The graph of a function f is is shown below.Sketch the graph of the derivative . ​ ​

Sketch a graph of the function over the interval . ​

Preparation for Calculus

Limits and Their Properties

Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

The graph of f is shown below.For which values of x is zero?

Find the points of inflection and discuss the concavity of the function on the interval .

The resistance R of a certain type of resistor is where R is measured in ohms and the temperature T is measured in degrees Celsius.Use a computer algebra system to find .

Given the following conditions for ,which graph best illustrates ? : The domain of the function is the real numbers,but ; ; ; . for all x where ,and does not exist at . for , for ,and does not exist at .

A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window (see figure).Find the dimensions of a Norman window of maximum area if the total perimeter is 38 feet.

Find the value of the derivative (if it exists)of at the indicated extremum.

Find all points of inflection of the graph of the function on the interval .Round your answer to three decimal places wherever applicable.

A rectangle is bounded by the x- and y-axes and the graph of (see figure).What length and width should the rectangle have so that its area is a maximum?

Use differentials to approximate the value of .Round your answer to four decimal places.

Compare and for at with Give your answers to four decimal places.

For the function ,how many of the inflection points of the function are also extrema?

Find all points of inflection,if any exist,of the graph of the function .Round your answers to two decimal places.

On a given day,the flow rate F (cars per hour)on a congested roadway is given by ,where v is the speed of the traffic in miles per hour.What speed will maximize the flow rate on the road? Round your answer to the nearest mile per hour.

Analyze and sketch a graph of the function .

Find the point on the graph of the function that is closest to the point .

Analyze the graph of the function .Determine any intercepts,relative extrema,points of inflection and asymptotes.Also determine where the graph is increasing or decreasing and concave up or concave down.Then identify the graph from the choices below.

Find all relative extrema of the function .Use the Second Derivative Test where applicable.

The graph of a function f is is shown below.Sketch the graph of the derivative .

Sketch a graph of the function over the interval .