Question 1

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 2

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 3

Determine which function "dominates", where we say that the function f(x) dominates the function g(x) as   if   and either   Show all work.

Accepted Answer

Both x^p and p^x increase without bound as @#IMG-DLM&

Question 4

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 5

Find the limit.

Accepted Answer

A)  1 
B)  3 
C)    
D)    
A)  1 
B)  3 
C)    
D)

Question 6

Sand is pouring from a pipe at the rate of 10 cubic feet per second. If the falling sand forms a conical pile so that its height is always   the diameter of the base, how fast is the height of the pile increasing when the height of the pile is 6 feet tall? Round answer to nearest hundredth.

Accepted Answer

A)  0.18 ft/sec 
B)  0.06 ft/sec 
C)  0.24 ft/sec 
D)  0.02 ft/sec 
A)  0.18 ft/sec 
B)  0.06 ft/sec 
C)  0.24 ft/sec 
D)  0.02 ft/sec

Question 7

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 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

Determine the equation of the slant asymptote of   .

Accepted Answer

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

Question 10

Approximate   accurate to 3 decimal places using Newton's method. State the function used.

Accepted Answer

A)  2.714 using   
B)  2.814 using   
C)  2.664 using   
D)  2.731 using   
A)  2.714 using   
B)  2.814 using   
C)  2.664 using   
D)  2.731 using

Question 11

Find all critical numbers. Then use a graph to determine whether the critical numbers represent a local maximum, local minimum, or neither.

Accepted Answer

A)    (local maximum),   (neither),   (local minimum) 
B)    (local maximum),   (local maximum),   (local minimum) 
C)    (local maximum),   (local minimum) 
D)    (local minimum),   (local maximum) 
A)    (local maximum),   (neither),   (local minimum) 
B)    (local maximum),   (local maximum),   (local minimum) 
C)    (local maximum),   (local minimum) 
D)    (local minimum),   (local maximum)

Question 12

A certain producer determines that his cost function is   . Determine the average cost of producing 1300 units. Round answer to the nearest penny.

Accepted Answer

A)  $3.91 
B)  $4.69 
C)  $5.63 
D)  $6.80 
A)  $3.91 
B)  $4.69 
C)  $5.63 
D)  $6.80

Question 13

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

Accepted Answer

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

Question 14

Explain why Newton's method fails for the following equation with the specified initial guess.

Accepted Answer

A)  Using   we see that f is not differentiable at   
B)  Using   we obtain   . 
C)  Using   we obtain   which will give   
D)  Using   we see that f does not have any real roots. 
A)  Using   we see that f is not differentiable at   
B)  Using   we obtain   . 
C)  Using   we obtain   which will give   
D)  Using   we see that f does not have any real roots.

Question 15

Sketch a graph of a function with the following properties.   if   if

Accepted Answer

The answer of Sketch a graph of a function with...

Question 16

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

Accepted Answer

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

Question 17

Find all critical numbers. Then use the graph to determine whether the critical numbers represent a local maximum, local minimum, or neither.

Accepted Answer

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

Question 18

A person in a rowboat 2 miles from the nearest point on a straight shoreline wishes to reach his house which is 6 miles farther down the shore. If he can row at a rate of 6 miles per hour and run at a rate of 10 miles per hour, what is the minimum amount of time (in minutes) it will take him to get home?

Accepted Answer

A)  68 minutes 
B)  45 minutes 
C)  52 minutes 
D)  73 minutes 
A)  68 minutes 
B)  45 minutes 
C)  52 minutes 
D)  73 minutes

Question 19

Water is pouring into a conical cistern at the rate of 18 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)  0.12 ft/min. 
B)  0.54 ft/min. 
C)  0.20 ft/min. 
D)  1.49 ft/min. 
A)  0.12 ft/min. 
B)  0.54 ft/min. 
C)  0.20 ft/min. 
D)  1.49 ft/min.

Question 20

A herd of sixty antelope is released onto a small game reserve so that their reproductive habits can be studied. In the beginning the population of the herd increases rapidly in size but eventually slows due to a dwindling food supply. Suppose the population of antelope after t years is given by the function   where   . Determine when the population begins to decline.

Accepted Answer

A)  14 years 
B)  16 years 
C)  17 years 
D)  18 years 
A)  14 years 
B)  16 years 
C)  17 years 
D)  18 years

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

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

Determine which function "dominates", where we say that the function f(x) dominates the function g(x) as if and either Show all work.

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

Find the limit.

Sand is pouring from a pipe at the rate of 10 cubic feet per second. If the falling sand forms a conical pile so that its height is always the diameter of the base, how fast is the height of the pile increasing when the height of the pile is 6 feet tall? Round answer to nearest hundredth.

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

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

Determine the equation of the slant asymptote of .

Approximate accurate to 3 decimal places using Newton's method. State the function used.

Find all critical numbers. Then use a graph to determine whether the critical numbers represent a local maximum, local minimum, or neither.

A certain producer determines that his cost function is . Determine the average cost of producing 1300 units. Round answer to the nearest penny.

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

Explain why Newton's method fails for the following equation with the specified initial guess.

Sketch a graph of a function with the following properties. if if

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

Find all critical numbers. Then use the graph to determine whether the critical numbers represent a local maximum, local minimum, or neither.

Water is pouring into a conical cistern at the rate of 18 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.

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

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

Determine which function "dominates", where we say that the function f(x) dominates the function g(x) as if and either Show all work.

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

Find the limit.

Sand is pouring from a pipe at the rate of 10 cubic feet per second. If the falling sand forms a conical pile so that its height is always the diameter of the base, how fast is the height of the pile increasing when the height of the pile is 6 feet tall? Round answer to nearest hundredth.

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

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

Determine the equation of the slant asymptote of .

Approximate accurate to 3 decimal places using Newton's method. State the function used.

Find all critical numbers. Then use a graph to determine whether the critical numbers represent a local maximum, local minimum, or neither.

A certain producer determines that his cost function is . Determine the average cost of producing 1300 units. Round answer to the nearest penny.

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

Explain why Newton's method fails for the following equation with the specified initial guess.

Sketch a graph of a function with the following properties. if if

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

Find all critical numbers. Then use the graph to determine whether the critical numbers represent a local maximum, local minimum, or neither.

Water is pouring into a conical cistern at the rate of 18 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.

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