Question 1

Estimate critical numbers and sketch graphs showing both global and local behavior.

Accepted Answer

critical numbers: @#IMG-DLM& @#IMG-DLM&

Question 2

Determine the following significant features of   , approximating if necessary, and sketch the graph.
a). intercepts
b). asymptotes
c). extrema
d). inflection points

Accepted Answer

@#IMG-DLM& a. Domain @#IMG-DLM& Range @#IMG-DLM& b. intercep

Question 3

Using a calculator or computer, estimate the absolute extrema of   , on the interval   .

Accepted Answer

A)  absolute max:   ; absolute min:   
B)  absolute max:   ; absolute min:   
C)  absolute max:   ; absolute min:   
D)  absolute max:   ; absolute min:   
A)  absolute max:   ; absolute min:   
B)  absolute max:   ; absolute min:   
C)  absolute max:   ; absolute min:   
D)  absolute max:   ; absolute min:

Question 4

Suppose that the charge in an electrical circuit is   . Find the current.

Accepted Answer

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

Question 5

Using Newton's method with   , determine the third iteration when approximating the root to at least six-digit accuracy of the following equation. x3 + x2 - 3x + 5 = 0

Accepted Answer

A)  -2.777778 
B)  -2.751101 
C)  -2.751145 
D)  -2.751446 
A)  -2.777778 
B)  -2.751101 
C)  -2.751145 
D)  -2.751446

Question 6

The total cost of producing and marketing x number of units of a certain product is given by   . For what number x is the total cost a minimum? Round answer to nearest unit.

Accepted Answer

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

Question 7

Find the point on the curve   closest to the point   . (Approximate the coordinates of the point to 3 decimal places.)

Accepted Answer

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

Question 8

Given the graph of   , locate the absolute extrema (if they exist) on the interval   .

Accepted Answer

A)  absolute max:  
Absolute min:   
B)  absolute min:   
C)  absolute max:  
Absolute min:   
D)  no absolute extrema 
A)  absolute max:  
Absolute min:   
B)  absolute min:   
C)  absolute max:  
Absolute min:   
D)  no absolute extrema

Question 9

Find the limit.

Accepted Answer

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

Question 10

Determine all critical numbers of   .

Accepted Answer

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

Question 11

Use Newton's method to find an approximate root of the equation   (accurate to six decimal places).

Accepted Answer

A)  0.186548 
B)  0.136548 
C)  0.056548 
D)  0.126548 
A)  0.186548 
B)  0.136548 
C)  0.056548 
D)  0.126548

Question 12

Given the graph of   , locate the absolute extrema (if they exist) on the interval   .

Accepted Answer

A)  absolute max:   
B)  absolute min:   and   
C)  absolute min:   
D)  no absolute extrema 
A)  absolute max:   
B)  absolute min:   and   
C)  absolute min:   
D)  no absolute extrema

Question 13

Estimate the intervals where the function shown below is concave up and/or concave down.

Accepted Answer

A)  concave up for  
Concave down for   
B)  concave up for  
Concave down for   
C)  concave up for  
Concave down for   
D)  concave up for  
Concave down for   
A)  concave up for  
Concave down for   
B)  concave up for  
Concave down for   
C)  concave up for  
Concave down for   
D)  concave up for  
Concave down for

Question 14

Find all critical numbers and use the First Derivative Test to classify each as a local maximum, local minimum, or neither.

Accepted Answer

A)  critical point:     (local maximum) 
B)  critical point:     (local minimum) 
C)  critical points:       (local minimum),   (local maximum) 
D)  critical points:         (local minimum),   (neither),   (local maximum) 
A)  critical point:     (local maximum) 
B)  critical point:     (local minimum) 
C)  critical points:       (local minimum),   (local maximum) 
D)  critical points:         (local minimum),   (neither),   (local maximum)

Question 15

Find the intervals where the function is increasing and decreasing. Use this information to determine all local extrema.

Accepted Answer

A)  decreasing:   increasing:   local maximum   
B)  decreasing:   increasing:   local minimum   
C)  decreasing:   no extrema 
D)  increasing:   no extrema 
A)  decreasing:   increasing:   local maximum   
B)  decreasing:   increasing:   local minimum   
C)  decreasing:   no extrema 
D)  increasing:   no extrema

Question 16

A certain producer determines that his cost function is   . Determine the marginal cost of producing 1500 units. Round answer to the nearest penny.

Accepted Answer

A)  $3.62 
B)  $1.61 
C)  $2.45 
D)  $1.73 
A)  $3.62 
B)  $1.61 
C)  $2.45 
D)  $1.73

Question 17

Using a calculator or computer, estimate the absolute extrema of   on the interval   . Round answer to the nearest hundredth.

Accepted Answer

A)  absolute max:   ; absolute min:   
B)  absolute max:   ; absolute min:   
C)  absolute max:   ; absolute min:   
D)  absolute max:   ; absolute min:   
A)  absolute max:   ; absolute min:   
B)  absolute max:   ; absolute min:   
C)  absolute max:   ; absolute min:   
D)  absolute max:   ; absolute min:

Question 18

Find the absolute extrema of the given function on the indicated interval.   on

Accepted Answer

A)  absolute maximum:   , absolute minimum:   
B)  absolute maximum:   , absolute minimum:   
C)  absolute maximum:   , absolute minimum:   
D)  absolute maximum:   , absolute minimum:   
A)  absolute maximum:   , absolute minimum:   
B)  absolute maximum:   , absolute minimum:   
C)  absolute maximum:   , absolute minimum:   
D)  absolute maximum:   , absolute minimum:

Question 19

Find the limit.

Accepted Answer

A)  0 
B)  1 
C)  -3 
D)  3 
A)  0 
B)  1 
C)  -3 
D)  3

Question 20

Determine all significant features by hand and sketch the graph of   .
a). intercepts
b). asymptotes
c). extrema
d). inflection points

Accepted Answer

@#IMG-DLM& ; x-int(s): x @#IMG-DLM& @#IMG-DLM& ; c

Estimate critical numbers and sketch graphs showing both global and local behavior.

Determine the following significant features of , approximating if necessary, and sketch the graph. a). intercepts b). asymptotes c). extrema d). inflection points

Using a calculator or computer, estimate the absolute extrema of , on the interval .

Suppose that the charge in an electrical circuit is . Find the current.

Using Newton's method with , determine the third iteration when approximating the root to at least six-digit accuracy of the following equation. x³ + x² - 3x + 5 = 0

The total cost of producing and marketing x number of units of a certain product is given by . For what number x is the total cost a minimum? Round answer to nearest unit.

Find the point on the curve closest to the point . (Approximate the coordinates of the point to 3 decimal places.)

Given the graph of , locate the absolute extrema (if they exist) on the interval .

Find the limit.

Determine all critical numbers of .

Use Newton's method to find an approximate root of the equation (accurate to six decimal places).

Given the graph of , locate the absolute extrema (if they exist) on the interval .

Estimate the intervals where the function shown below is concave up and/or concave down.

Find all critical numbers and use the First Derivative Test to classify each as a local maximum, local minimum, or neither.

Find the intervals where the function is increasing and decreasing. Use this information to determine all local extrema.

A certain producer determines that his cost function is . Determine the marginal cost of producing 1500 units. Round answer to the nearest penny.

Using a calculator or computer, estimate the absolute extrema of on the interval . Round answer to the nearest hundredth.

Find the absolute extrema of the given function on the indicated interval. on

Find the limit.

Determine all significant features by hand and sketch the graph of . a). intercepts b). asymptotes c). extrema d). inflection points

Preliminaries

Limits and Continuity

Differentiation

Integration

Applications of the Definite Integral

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Exam 4: Applications of the Derivative

Estimate critical numbers and sketch graphs showing both global and local behavior.

Determine the following significant features of , approximating if necessary, and sketch the graph. a). intercepts b). asymptotes c). extrema d). inflection points

Using a calculator or computer, estimate the absolute extrema of , on the interval .

Suppose that the charge in an electrical circuit is . Find the current.

Using Newton's method with , determine the third iteration when approximating the root to at least six-digit accuracy of the following equation. x3 + x2 - 3x + 5 = 0

The total cost of producing and marketing x number of units of a certain product is given by . For what number x is the total cost a minimum? Round answer to nearest unit.

Find the point on the curve closest to the point . (Approximate the coordinates of the point to 3 decimal places.)

Given the graph of , locate the absolute extrema (if they exist) on the interval .

Find the limit.

Determine all critical numbers of .

Use Newton's method to find an approximate root of the equation (accurate to six decimal places).

Given the graph of , locate the absolute extrema (if they exist) on the interval .

Estimate the intervals where the function shown below is concave up and/or concave down.

Find all critical numbers and use the First Derivative Test to classify each as a local maximum, local minimum, or neither.

Find the intervals where the function is increasing and decreasing. Use this information to determine all local extrema.

A certain producer determines that his cost function is . Determine the marginal cost of producing 1500 units. Round answer to the nearest penny.

Using a calculator or computer, estimate the absolute extrema of on the interval . Round answer to the nearest hundredth.

Find the absolute extrema of the given function on the indicated interval. on

Find the limit.

Determine all significant features by hand and sketch the graph of . a). intercepts b). asymptotes c). extrema d). inflection points

Preliminaries

Limits and Continuity

Differentiation

Integration

Applications of the Definite Integral

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Using Newton's method with , determine the third iteration when approximating the root to at least six-digit accuracy of the following equation. x³ + x² - 3x + 5 = 0