Question 1

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

Accepted Answer

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

Question 2

Determine all critical numbers of   .

Accepted Answer

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

Question 3

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 4

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 5

Graph the function and completely discuss the graph. Round answers to three decimals places, if necessary.

Accepted Answer

A)  domain:   vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: (0, 0), (14, -121.985); concave down:   ;
Concave up:   ; x-intercepts: (0, 0) and (35, 0)   
B)  domain:   vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: (0, 0), (14, -121.985); concave up:  
X-intercepts: (0, 0) and (35, 0)   
C)  domain:   vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: x = 0; local extrema: (0, 0), (14, -121.985); concave up:  
X-intercepts: (0, 0) and (35, 0)   
D)  domain:   vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: x = 0; local extrema: (0, 0), (14, -121.985); concave down:   ;
Concave up:   ; x-intercepts: (0, 0) and (35, 0)   
A)  domain:   vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: (0, 0), (14, -121.985); concave down:   ;
Concave up:   ; x-intercepts: (0, 0) and (35, 0)   
B)  domain:   vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: (0, 0), (14, -121.985); concave up:  
X-intercepts: (0, 0) and (35, 0)   
C)  domain:   vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: x = 0; local extrema: (0, 0), (14, -121.985); concave up:  
X-intercepts: (0, 0) and (35, 0)   
D)  domain:   vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: x = 0; local extrema: (0, 0), (14, -121.985); concave down:   ;
Concave up:   ; x-intercepts: (0, 0) and (35, 0)

Question 6

Find the volume of the largest box with no top that can be made from a piece of cardboard 60 inches square by cutting equal squares from the corners and turning up the sides.

Accepted Answer

A)  16,000 in3 
B)  1000 in3 
C)  24,000 in3 
D)  8000 in3 
A)  16,000 in3 
B)  1000 in3 
C)  24,000 in3 
D)  8000 in3

Question 7

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 8

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 7 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 9

A handbill is to contain 98 square inches of printed material, with 4-inch margins at the top and bottom and 2-inch margins on each side. What dimensions for the handbill would use the least amount of paper?

Accepted Answer

A)  10 inches by 19 inches 
B)  5 inches by 24 inches 
C)  11 inches by 22 inches 
D)  16 inches by 25 inches 
A)  10 inches by 19 inches 
B)  5 inches by 24 inches 
C)  11 inches by 22 inches 
D)  16 inches by 25 inches

Question 10

Find all asymptotes and extrema and sketch a graph.

Accepted Answer

vertical asymptotes:

Question 11

Graph   and its slant asymptote on the same set of axes.

Accepted Answer

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

Question 12

Find the x-coordinates of all extrema and sketch the graph of   showing global and local behavior. Round answer to nearest thousandth.

Accepted Answer

@#IMG-DLM& is a loca

Question 13

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

Accepted Answer

A)  10 units 
B)  177 units 
C)  208 units 
D)  85 units 
A)  10 units 
B)  177 units 
C)  208 units 
D)  85 units

Question 14

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 15

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 16

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 17

A boy standing on a cliff is watching a boat through a telescope as it approaches the base of the cliff directly below him. If the telescope is 250 feet above water level and the boat is approaching at 25 feet per second, at what rate is the angle of the telescope changing when the boat is 250 feet away?

Accepted Answer

A)    radians per second 
B)    radians per second 
C)    radians per second 
D)    radians per second 
A)    radians per second 
B)    radians per second 
C)    radians per second 
D)    radians per second

Question 18

Use Newton's method with x0 = 2.6 to compute x1 and x2 without the use of a calculator.
f(x) = x3 - 3x - 5

Accepted Answer

x<sub>0</sub> = 2.6

Question 19

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 20

A certain producer determines that his cost function is   . Determine the marginal cost of producing 1400 units. Round answer to the nearest penny.

Accepted Answer

A)  $2.59 
B)  $0.58 
C)  $1.42 
D)  $0.70 
A)  $2.59 
B)  $0.58 
C)  $1.42 
D)  $0.70

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

Determine all critical numbers of .

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

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

Graph the function and completely discuss the graph. Round answers to three decimals places, if necessary.

Find the volume of the largest box with no top that can be made from a piece of cardboard 60 inches square by cutting equal squares from the corners and turning up the sides.

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 handbill is to contain 98 square inches of printed material, with 4-inch margins at the top and bottom and 2-inch margins on each side. What dimensions for the handbill would use the least amount of paper?

Find all asymptotes and extrema and sketch a graph.

Graph and its slant asymptote on the same set of axes.

Find the x-coordinates of all extrema and sketch the graph of showing global and local behavior. Round answer to nearest thousandth.

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

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

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

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

Use Newton's method with x₀ = 2.6 to compute x₁ and x₂without the use of a calculator. f(x) = x³ - 3x - 5

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

A certain producer determines that his cost function is . Determine the marginal cost of producing 1400 units. Round answer to the nearest penny.

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

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

Determine all critical numbers of .

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

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

Graph the function and completely discuss the graph. Round answers to three decimals places, if necessary.

Find the volume of the largest box with no top that can be made from a piece of cardboard 60 inches square by cutting equal squares from the corners and turning up the sides.

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 handbill is to contain 98 square inches of printed material, with 4-inch margins at the top and bottom and 2-inch margins on each side. What dimensions for the handbill would use the least amount of paper?

Find all asymptotes and extrema and sketch a graph.

Graph and its slant asymptote on the same set of axes.

Find the x-coordinates of all extrema and sketch the graph of showing global and local behavior. Round answer to nearest thousandth.

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

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

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

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

Use Newton's method with x0 = 2.6 to compute x1 and x2 without the use of a calculator. f(x) = x3 - 3x - 5

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

A certain producer determines that his cost function is . Determine the marginal cost of producing 1400 units. Round answer to the nearest penny.

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

Use Newton's method with x₀ = 2.6 to compute x₁ and x₂without the use of a calculator. f(x) = x³ - 3x - 5