Question 1

Graph the function and completely discuss the graph.

Accepted Answer

domain:   vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none;
local extrema:   , k any integer (local minima),   , k any integer (local maxima);
concave down:   concave up:   x-intercept:   k any integer; y-intercept:

Question 2

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

Accepted Answer

A)  $8.13 and higher 
B)  $7.50 and higher 
C)  $0 to $8.75 
D)  $0 to $10.00 
A)  $8.13 and higher 
B)  $7.50 and higher 
C)  $0 to $8.75 
D)  $0 to $10.00 B

Question 3

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 4

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

Accepted Answer

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

Question 5

Water is pouring into a conical cistern at the rate of 16 cubic feet per minute. If the height of the cistern is 21 feet and the radius of its circular opening is 7 feet, how fast is the water level rising when the water is 16 feet deep? Round answer to nearest hundredth.

Accepted Answer

A)  0.10 ft/min. 
B)  0.52 ft/min. 
C)  0.18 ft/min. 
D)  1.47 ft/min. 
A)  0.10 ft/min. 
B)  0.52 ft/min. 
C)  0.18 ft/min. 
D)  1.47 ft/min.

Question 6

Find the linear approximation at x = 0 for each of f (x) = (x + 1)2 + 5, g(x) = 6 + sin(2x) and   . Graph each function together with its linear approximation.

Accepted Answer

For all three functi

Question 7

Sketch the graph with the given properties.     for all x,     for     for

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

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 10

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

Accepted Answer

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

Question 11

Find a function whose graph has the given asymptotes.     and

Accepted Answer

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

Question 12

Given   , on the interval   , determine the critical number(s).

Accepted Answer

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

Question 13

Bubba, a farmer, wants to fence-in a three-sided area next to his barn, using the side of the barn as the fourth side of the rectangle. He also wants to divide this rectangular area into three identical pens (see figure below). If Bubba has 104 feet of available fencing, then each pen will have what dimensions in order to maximize its area? Round dimensions to nearest tenth.

Accepted Answer

A)  52 ft   26 ft 
B)  26 ft   26 ft 
C)  52 ft   13 ft 
D)  26 ft   13 ft 
A)  52 ft   26 ft 
B)  26 ft   26 ft 
C)  52 ft   13 ft 
D)  26 ft   13 ft

Question 14

Find all critical numbers.

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

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 17

Suppose that a population grows according to the logistics equation   . Find the population at which the population growth rate is a maximum.

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

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 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

Graph the function and completely discuss the graph.

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

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.

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

Water is pouring into a conical cistern at the rate of 16 cubic feet per minute. If the height of the cistern is 21 feet and the radius of its circular opening is 7 feet, how fast is the water level rising when the water is 16 feet deep? Round answer to nearest hundredth.

Find the linear approximation at x = 0 for each of f (x) = (x + 1)² + 5, g(x) = 6 + sin(2x) and . Graph each function together with its linear approximation.

Sketch the graph with the given properties. for all x, for for

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

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.

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

Find a function whose graph has the given asymptotes. and

Given , on the interval , determine the critical number(s).

Find all critical numbers.

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

Suppose that a population grows according to the logistics equation . Find the population at which the population growth rate is a maximum.

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

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.

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

Exponentials, Logarithms and Other Transcendental Functions

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

Graph the function and completely discuss the graph.

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

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.

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

Water is pouring into a conical cistern at the rate of 16 cubic feet per minute. If the height of the cistern is 21 feet and the radius of its circular opening is 7 feet, how fast is the water level rising when the water is 16 feet deep? Round answer to nearest hundredth.

Find the linear approximation at x = 0 for each of f (x) = (x + 1)2 + 5, g(x) = 6 + sin(2x) and . Graph each function together with its linear approximation.

Sketch the graph with the given properties. for all x, for for

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

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.

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

Find a function whose graph has the given asymptotes. and

Given , on the interval , determine the critical number(s).

Find all critical numbers.

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

Suppose that a population grows according to the logistics equation . Find the population at which the population growth rate is a maximum.

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

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.

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

Exponentials, Logarithms and Other Transcendental Functions

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 at x = 0 for each of f (x) = (x + 1)² + 5, g(x) = 6 + sin(2x) and . Graph each function together with its linear approximation.

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