Question 1

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

Accepted Answer

A)    
B) 0 
C)    
D)    
E) does not exist 
A)    
B) 0 
C)    
D)    
E) does not exist

Question 2

Locate the absolute extrema of the function   on the closed interval   . ​

Accepted Answer

A) absolute max:   ;no absolute min 
B) no absolute max or min 
C) no absolute max;absolute min:   
D) absolute max:   ;absolute min:
  
E) absolute max:   ;absolute min:
  
A) absolute max:   ;no absolute min 
B) no absolute max or min 
C) no absolute max;absolute min:   
D) absolute max:   ;absolute min:
  
E) absolute max:   ;absolute min:

Question 3

A valve on a storage tank is opened for 4 hours to release a chemical in a manufacturing process.The flow rate R (in liters per hour)at time t (in hours)is given by the linear model   .Write the linear model in exponential form.Round to four decimal places. ​

Accepted Answer

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

Question 4

The function   is defined as   on the open interval (-3,3)as illustrated in the graph shown.​
​  
-Determine the coordinates of the relative extrema of   in the open interval (-3,3).

Accepted Answer

Given: @#IMG-DLM& and @#IMG-DLM& ​ @#IMG-DLM& ​
-3 < x < -1
-1 < x < 1

Question 5

The height of an object t seconds after it is dropped from a height of 600 meters is   .Find the time during the first 12 seconds of fall at which the instantaneous velocity equals the average velocity.Round to two decimal places,if necessary. ​

Accepted Answer

A) 72 seconds 
B) 29.4 seconds 
C) 10.2 seconds 
D) 6 seconds 
E) 2.45 seconds 
A) 72 seconds 
B) 29.4 seconds 
C) 10.2 seconds 
D) 6 seconds 
E) 2.45 seconds

Question 6

A company introduces a new product for which the number of units sold S is   where t is the time in months since the product was introduced.During what month does   equal the average value of   during the first year? ​

Accepted Answer

A) September 
B) April 
C) November 
D) May 
E) March 
A) September 
B) April 
C) November 
D) May 
E) March

Question 7

The graph of f is shown below.For which value of x is   minimum? ​   ​

Accepted Answer

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

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

Locate the absolute extrema of the function on the closed interval .

A valve on a storage tank is opened for 4 hours to release a chemical in a manufacturing process.The flow rate R (in liters per hour)at time t (in hours)is given by the linear model .Write the linear model in exponential form.Round to four decimal places.

The function is defined as on the open interval (-3,3)as illustrated in the graph shown. -Determine the coordinates of the relative extrema of in the open interval (-3,3).

The height of an object t seconds after it is dropped from a height of 600 meters is .Find the time during the first 12 seconds of fall at which the instantaneous velocity equals the average velocity.Round to two decimal places,if necessary.

A company introduces a new product for which the number of units sold S is where t is the time in months since the product was introduced.During what month does equal the average value of during the first year?

The graph of f is shown below.For which value of x is minimum?

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

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

Locate the absolute extrema of the function on the closed interval . ​

A valve on a storage tank is opened for 4 hours to release a chemical in a manufacturing process.The flow rate R (in liters per hour)at time t (in hours)is given by the linear model .Write the linear model in exponential form.Round to four decimal places. ​

The function is defined as on the open interval (-3,3)as illustrated in the graph shown.​ ​ -Determine the coordinates of the relative extrema of in the open interval (-3,3).

The height of an object t seconds after it is dropped from a height of 600 meters is .Find the time during the first 12 seconds of fall at which the instantaneous velocity equals the average velocity.Round to two decimal places,if necessary. ​

A company introduces a new product for which the number of units sold S is where t is the time in months since the product was introduced.During what month does equal the average value of during the first year? ​

The graph of f is shown below.For which value of x is minimum? ​ ​