Question 1

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

Accepted Answer

A)  ​The relative maximum is   
B)  ​​The relative minimum is   
C)  ​​The relative maximum is   
D)  ​​​The relative minimum is   
E)  ​​The relative maximum is   
A)  ​The relative maximum is   
B)  ​​The relative minimum is   
C)  ​​The relative maximum is   
D)  ​​​The relative minimum is   
E)  ​​The relative maximum is

Question 2

Find the x-values (if any)at which the function   is not continuous.Are the discontinuities removable? ​

Accepted Answer

A)  continuous everywhere 
B)  not removable 
C)  discontinuous everywhere 
D)  removable 
E)  none of the above 
A)  continuous everywhere 
B)  not removable 
C)  discontinuous everywhere 
D)  removable 
E)  none of the above

Question 3

Assume that the number (in millions)of basic cable television subscribers in the United States from 1996 through 2005 is given in the following table.Use a graphing utility to graph a scatter plot of the given data.Describe any trends that appear within the last four years.

Accepted Answer

A)  ​  
​The number of subscribers appears to be increasing. 
B)  ​  
The number of subscribers appears to be decreasing. 
C)  ​  
The number of subscribers appears to be linearly decreasing. 
D)  ​  
The number of subscribers appears to be decreasing 
E)  ​   ​
The number of subscribers appears to be linearly increasing. 
A)  ​  
​The number of subscribers appears to be increasing. 
B)  ​  
The number of subscribers appears to be decreasing. 
C)  ​  
The number of subscribers appears to be linearly decreasing. 
D)  ​  
The number of subscribers appears to be decreasing 
E)  ​   ​
The number of subscribers appears to be linearly increasing.

Question 4

​Find the second derivative of the function   ​

Accepted Answer

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

Question 5

​A firm can produce 100 units per week.If its total cost function is   dollars,and its total revenue function is   dollars,find the maximum profit. ​

Accepted Answer

A)  ​$3,679 
B)  ​$1,600 
C)  ​$7,031 
D)  ​$1,265 
E)  ​$1,941 
A)  ​$3,679 
B)  ​$1,600 
C)  ​$7,031 
D)  ​$1,265 
E)  ​$1,941

Question 6

​Find the slope of the graph at the given point. ​   ​   ​

Accepted Answer

A)  ​0 
B)  ​3 
C)  ​5 
D)  ​4 
E)  ​7 
A)  ​0 
B)  ​3 
C)  ​5 
D)  ​4 
E)  ​7

Question 7

​Find the derivative of the function   ​

Accepted Answer

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

Question 8

Find the distance between the points (-2,-5)and (-7,-10).Round your answer to the nearest hundredth if necessary. ​

Accepted Answer

A)  17.49 
B)  0 
C)  7.07 
D)  3.16 
E)  50 
A)  17.49 
B)  0 
C)  7.07 
D)  3.16 
E)  50

Question 9

​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 10

​Find the differential dy of the function   ​

Accepted Answer

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

Question 11

​Use the demand function   to find the rate of change in the demand x for the given price   Round your answer to two decimal places. ​

Accepted Answer

A)  ​1.44 units per dollar 
B)  ​-0.72 units per dollar 
C)  ​0.72 units per dollar 
D)  ​0.96 units per dollar 
E)  ​-1.44 units per dollar 
A)  ​1.44 units per dollar 
B)  ​-0.72 units per dollar 
C)  ​0.72 units per dollar 
D)  ​0.96 units per dollar 
E)  ​-1.44 units per dollar

Question 12

​p is in dollars and q is the number of units.Find the elasticity of the demand function   at the price   ​

Accepted Answer

A)  ​-4.04 
B)  ​1.00 
C)  ​4.04 
D)  ​-0.78 
E)  ​0.78 
A)  ​-4.04 
B)  ​1.00 
C)  ​4.04 
D)  ​-0.78 
E)  ​0.78

Question 13

​Find the indicated derivative. ​
Find   if   ​

Accepted Answer

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

Question 14

​Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 15

Use the graph of   to sketch   ​ ​

Accepted Answer

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

Question 16

​A manufacturer of DVD players has monthly fixed costs of $9000 and variable costs of $45 per unit for one particular model.For this model DVD player,find the function   for monthly total costs where ​x denotes the number of units produced and sold. ​

Accepted Answer

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

Question 17

​Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 18

​The average typing speed N (in words per minute)after t weeks of lessons is modeled by   Find the rate at which the typing speed is changing when   weeks.Round your answer to two decimal places. ​

Accepted Answer

A)  ​1.51 words/min/week 
B)  ​2.15 words/min/week 
C)  ​2.51 words/min/week 
D)  ​4.38 words/min/week 
E)  ​5.04 words/min/week 
A)  ​1.51 words/min/week 
B)  ​2.15 words/min/week 
C)  ​2.51 words/min/week 
D)  ​4.38 words/min/week 
E)  ​5.04 words/min/week

Question 19

​Find the absolute extrema of the function   on the closed interval   Round your answer to two decimal places. ​

Accepted Answer

A)  ​The maximum of the function is 1 and the minimum of the function is 0. 
B)  ​The maximum of the function is 2.92 and the minimum of the function is 1. 
C)  ​The maximum of the function is 2.92 and the minimum of the function is 0. 
D)  ​The maximum of the function is1 and the minimum of the function is 2.52. 
E)  ​The maximum of the function is 0 and the minimum of the function is 2.52. 
A)  ​The maximum of the function is 1 and the minimum of the function is 0. 
B)  ​The maximum of the function is 2.92 and the minimum of the function is 1. 
C)  ​The maximum of the function is 2.92 and the minimum of the function is 0. 
D)  ​The maximum of the function is1 and the minimum of the function is 2.52. 
E)  ​The maximum of the function is 0 and the minimum of the function is 2.52.

Question 20

The management of a factory finds that the maximum number of units a worker can produce in a day is 30.The learning curve for the number of units N produced per day after a new employee has worked days is modeled by   After 20 days on the job,a worker is producing 19 units in a day.How many days should pass before this worker is producing 25 units per day? ​

Accepted Answer

A)  about 36 days. 
B)  about 45 days. 
C)  about 30 days. 
D)  about 10 days. 
A)  about 36 days. 
B)  about 45 days. 
C)  about 30 days. 
D)  about 10 days.

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

Find the x-values (if any)at which the function is not continuous.Are the discontinuities removable?

Assume that the number (in millions)of basic cable television subscribers in the United States from 1996 through 2005 is given in the following table.Use a graphing utility to graph a scatter plot of the given data.Describe any trends that appear within the last four years.

Find the second derivative of the function

A firm can produce 100 units per week.If its total cost function is dollars,and its total revenue function is dollars,find the maximum profit.

Find the slope of the graph at the given point.

Find the derivative of the function

Find the distance between the points (-2,-5)and (-7,-10).Round your answer to the nearest hundredth if necessary.

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

Find the differential dy of the function

Use the demand function to find the rate of change in the demand x for the given price Round your answer to two decimal places.

p is in dollars and q is the number of units.Find the elasticity of the demand function at the price

Find the indicated derivative. Find if

Find the derivative of the following function.

Use the graph of to sketch

A manufacturer of DVD players has monthly fixed costs of $9000 and variable costs of $45 per unit for one particular model.For this model DVD player,find the function for monthly total costs where x denotes the number of units produced and sold.

Find the derivative of the following function.

The average typing speed N (in words per minute)after t weeks of lessons is modeled by Find the rate at which the typing speed is changing when weeks.Round your answer to two decimal places.

Find the absolute extrema of the function on the closed interval Round your answer to two decimal places.

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

Exam 1: Functions, graphs, and Limits

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

Find the x-values (if any)at which the function is not continuous.Are the discontinuities removable? ​

Assume that the number (in millions)of basic cable television subscribers in the United States from 1996 through 2005 is given in the following table.Use a graphing utility to graph a scatter plot of the given data.Describe any trends that appear within the last four years.

​Find the second derivative of the function ​

​A firm can produce 100 units per week.If its total cost function is dollars,and its total revenue function is dollars,find the maximum profit. ​

​Find the slope of the graph at the given point. ​ ​ ​

​Find the derivative of the function ​

Find the distance between the points (-2,-5)and (-7,-10).Round your answer to the nearest hundredth if necessary. ​

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

​Find the differential dy of the function ​

​Use the demand function to find the rate of change in the demand x for the given price Round your answer to two decimal places. ​

​p is in dollars and q is the number of units.Find the elasticity of the demand function at the price ​

​Find the indicated derivative. ​ Find if ​

​Find the derivative of the following function. ​ ​

Use the graph of to sketch ​ ​

​A manufacturer of DVD players has monthly fixed costs of $9000 and variable costs of $45 per unit for one particular model.For this model DVD player,find the function for monthly total costs where ​x denotes the number of units produced and sold. ​

​Find the derivative of the following function. ​ ​

​The average typing speed N (in words per minute)after t weeks of lessons is modeled by Find the rate at which the typing speed is changing when weeks.Round your answer to two decimal places. ​

​Find the absolute extrema of the function on the closed interval Round your answer to two decimal places. ​

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

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

Find the x-values (if any)at which the function is not continuous.Are the discontinuities removable?

Find the second derivative of the function

A firm can produce 100 units per week.If its total cost function is dollars,and its total revenue function is dollars,find the maximum profit.

Find the slope of the graph at the given point.

Find the derivative of the function

Find the distance between the points (-2,-5)and (-7,-10).Round your answer to the nearest hundredth if necessary.

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

Find the differential dy of the function

Use the demand function to find the rate of change in the demand x for the given price Round your answer to two decimal places.

p is in dollars and q is the number of units.Find the elasticity of the demand function at the price

Find the indicated derivative. Find if

Find the derivative of the following function.

Use the graph of to sketch

A manufacturer of DVD players has monthly fixed costs of $9000 and variable costs of $45 per unit for one particular model.For this model DVD player,find the function for monthly total costs where x denotes the number of units produced and sold.

Find the derivative of the following function.

The average typing speed N (in words per minute)after t weeks of lessons is modeled by Find the rate at which the typing speed is changing when weeks.Round your answer to two decimal places.

Find the absolute extrema of the function on the closed interval Round your answer to two decimal places.