Question 1

Use linear approximation of   at   to estimate the quantity of   to the nearest ten thousandth.

Accepted Answer

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

Question 2

Graph the function and completely discuss the graph.

Accepted Answer

domain: @#IMG-DLM& vertical asymptote: @#IMG-DLM&

Question 3

Sketch the graph of   while answering the following questions.
a. What is the domain and range of   ?
b. What are the intercepts of   ?
c. What, if any, are the equation(s) of vertical asymptotes of   ?
d. What, if any, are the local min(s) and local max(s) of   ?
e. What, if any, are the inflection point(s) of   ?
f. What, if it exists, is the equation of the horizontal asymptote of  ?

Accepted Answer

@#IMG-DLM& a. Domain @#IMG-DLM& Range @#IMG-DLM& b. @#IMG-DLM& c. no v

Question 4

Using the critical numbers of   , use the Second Derivative Test to determine all local extrema.

Accepted Answer

A)  critical numbers:   ; local max   ; local min   
B)  critical numbers:   ; local max   ; local min   
C)  critical numbers:   ; local max   ; local min   
D)  critical numbers:   ; local max   ; local min   
A)  critical numbers:   ; local max   ; local min   
B)  critical numbers:   ; local max   ; local min   
C)  critical numbers:   ; local max   ; local min   
D)  critical numbers:   ; local max   ; local min

Question 5

Using Newton's method, approximate the root of the following equation to at least six-digit accuracy.

Accepted Answer

A)  0.817880 
B)  0.839580 
C)  0.807714 
D)  0.827880 
A)  0.817880 
B)  0.839580 
C)  0.807714 
D)  0.827880

Question 6

Suppose that at the price   dollars the demand for a product is inelastic. If the price is increased, what will happen to revenue?

Accepted Answer

A)  increase 
B)  decrease 
C)  stay the same 
A)  increase 
B)  decrease 
C)  stay the same

Question 7

Determine the following 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& ; vertical asy

Question 8

Determine, by hand, the interval(s) where   is increasing and/or decreasing.

Accepted Answer

A)    
B)  increasing   ; decreasing   
C)  increasing   ; decreasing   
D)  increasing   ; decreasing   
A)    
B)  increasing   ; decreasing   
C)  increasing   ; decreasing   
D)  increasing   ; decreasing

Question 9

A plane is located at   miles (horizontally) away from an airport at an altitude of 6 miles and maintains a constant altitude. Radar at the airport detects that the distance   between the plane and airport is changing at a rate of   mph. What is the speed   of the airplane?

Accepted Answer

The answer of A plane is located at  ...

Question 10

The mass of the first x meters of a thin rod is given by the function   grams for   Find the linear mass density function for the rod and determine whether the composition of the rod is homogeneous or nonhomogeneous.

Accepted Answer

A)    nonhomogeneous 
B)    homogeneous 
C)    nonhomogeneous 
D)    homogeneous 
A)    nonhomogeneous 
B)    homogeneous 
C)    nonhomogeneous 
D)    homogeneous

Question 11

A certain company estimates that it can sell f(x)-thousand video game consoles at the price of $x as given in the table.   Use a linear approximation to estimate the number of consoles that can be sold at $62.

Accepted Answer

A)  approximately 106 thousand consoles 
B)  approximately 109 thousand consoles 
C)  approximately 131 thousand consoles 
D)  approximately 139 thousand consoles 
A)  approximately 106 thousand consoles 
B)  approximately 109 thousand consoles 
C)  approximately 131 thousand consoles 
D)  approximately 139 thousand consoles

Question 12

A water line runs east-west. A town wants to connect two new housing developments to the line by running lines from a single point on the existing line to the two developments. The first development is 5 miles south of the existing line; the other development is 6 miles south of the existing line and 3 miles east of the first development. How many miles east from the point due north of the first development should the connection be made to minimize the total length of new line?

Accepted Answer

A)  0 miles 
B)  3 miles 
C)    miles 
D)  1.5 miles 
E)    miles 
A)  0 miles 
B)  3 miles 
C)    miles 
D)  1.5 miles 
E)    miles

Question 13

Given   determine if the critical number   represents a local maximum, local minimum or neither.

Accepted Answer

A)  local maximum 
B)  local minimum 
C)  neither 
A)  local maximum 
B)  local minimum 
C)  neither

Question 14

If   , find the range of prices for which the demand is inelastic. Round answer to nearest penny.

Accepted Answer

A)  $36.25 and higher 
B)  $45.00 and higher 
C)  $0 to $27.50 
D)  $0 to $10.00 
A)  $36.25 and higher 
B)  $45.00 and higher 
C)  $0 to $27.50 
D)  $0 to $10.00

Question 15

Determine, by hand, the interval(s) where   is increasing and/or decreasing.

Accepted Answer

A)  increasing   ; decreasing   
B)  increasing   and   ; decreasing   and   
C)  increasing   and   ; decreasing   and   
D)  increasing   and   ; decreasing   
A)  increasing   ; decreasing   
B)  increasing   and   ; decreasing   and   
C)  increasing   and   ; decreasing   and   
D)  increasing   and   ; decreasing

Question 16

Given the graph of f(x), draw in the tangent lines used in Newton's method to determine x1 and x2 after starting at x0 = 1.

Accepted Answer

The answer of Given the graph of f(x), draw in...

Question 17

Determine the level of production that minimizes the average cost if the cost function is   . Round answer to nearest whole number.

Accepted Answer

A)  20 units 
B)  235 units 
C)  183 units 
D)  95 units 
A)  20 units 
B)  235 units 
C)  183 units 
D)  95 units

Question 18

Find the linear approximation, L(x), to f(x) at x = x0.

Accepted Answer

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

Question 19

Determine all critical numbers of   .

Accepted Answer

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

Question 20

Determine all significant features on the interval   (approximately where necessary) and sketch the graph on the interval.

Accepted Answer

domain: @#IMG-DLM& vertical asymptotes: none; hori

Use linear approximation of at to estimate the quantity of to the nearest ten thousandth.

Graph the function and completely discuss the graph.

Using the critical numbers of , use the Second Derivative Test to determine all local extrema.

Using Newton's method, approximate the root of the following equation to at least six-digit accuracy.

Suppose that at the price dollars the demand for a product is inelastic. If the price is increased, what will happen to revenue?

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

Determine, by hand, the interval(s) where is increasing and/or decreasing.

A plane is located at miles (horizontally) away from an airport at an altitude of 6 miles and maintains a constant altitude. Radar at the airport detects that the distance between the plane and airport is changing at a rate of mph. What is the speed of the airplane?

The mass of the first x meters of a thin rod is given by the function grams for Find the linear mass density function for the rod and determine whether the composition of the rod is homogeneous or nonhomogeneous.

A certain company estimates that it can sell f(x)-thousand video game consoles at the price of $x as given in the table. Use a linear approximation to estimate the number of consoles that can be sold at $62.

Given determine if the critical number represents a local maximum, local minimum or neither.

If , find the range of prices for which the demand is inelastic. Round answer to nearest penny.

Determine, by hand, the interval(s) where is increasing and/or decreasing.

Given the graph of f(x), draw in the tangent lines used in Newton's method to determine x₁ and x₂ after starting at x₀ = 1.

Determine the level of production that minimizes the average cost if the cost function is . Round answer to nearest whole number.

Find the linear approximation, L(x), to f(x) at x = x₀.

Determine all critical numbers of .

Determine all significant features on the interval (approximately where necessary) and sketch the graph on the interval.

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

Use linear approximation of at to estimate the quantity of to the nearest ten thousandth.

Graph the function and completely discuss the graph.

Using the critical numbers of , use the Second Derivative Test to determine all local extrema.

Using Newton's method, approximate the root of the following equation to at least six-digit accuracy.

Suppose that at the price dollars the demand for a product is inelastic. If the price is increased, what will happen to revenue?

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

Determine, by hand, the interval(s) where is increasing and/or decreasing.

A plane is located at miles (horizontally) away from an airport at an altitude of 6 miles and maintains a constant altitude. Radar at the airport detects that the distance between the plane and airport is changing at a rate of mph. What is the speed of the airplane?

The mass of the first x meters of a thin rod is given by the function grams for Find the linear mass density function for the rod and determine whether the composition of the rod is homogeneous or nonhomogeneous.

A certain company estimates that it can sell f(x)-thousand video game consoles at the price of $x as given in the table. Use a linear approximation to estimate the number of consoles that can be sold at $62.

Given determine if the critical number represents a local maximum, local minimum or neither.

If , find the range of prices for which the demand is inelastic. Round answer to nearest penny.

Determine, by hand, the interval(s) where is increasing and/or decreasing.

Given the graph of f(x), draw in the tangent lines used in Newton's method to determine x1 and x2 after starting at x0 = 1.

Determine the level of production that minimizes the average cost if the cost function is . Round answer to nearest whole number.

Find the linear approximation, L(x), to f(x) at x = x0.

Determine all critical numbers of .

Determine all significant features on the interval (approximately where necessary) and sketch the graph on the interval.

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

Given the graph of f(x), draw in the tangent lines used in Newton's method to determine x₁ and x₂ after starting at x₀ = 1.

Find the linear approximation, L(x), to f(x) at x = x₀.