Question 1

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 2

A point   moves on the graph of the equation   so that the x-coordinate changes at a rate of 2 units per second. How fast is the y-coordinate changing at the point

Accepted Answer

A)  115 units/sec 
B)  120 units/sec 
C)  125 units/sec 
D)  130 units/sec 
A)  115 units/sec 
B)  120 units/sec 
C)  125 units/sec 
D)  130 units/sec

Question 3

Determine all significant features and sketch a graph.

Accepted Answer

domain: @#IMG-DLM& x-intercepts: @#IMG-DLM& @#IMG-DLM& y-int

Question 4

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 5

A company's revenue for selling x (thousand) items is given by   in millions of dollars. Find the value of x (rounded to the nearest item) that maximizes the revenue and find the maximum revenue (rounded to the nearest dollar).

Accepted Answer

A)  5481 items; maximum revenue: $2,740,370 
B)  7481 items; maximum revenue: $2,586,033 
C)  20,500 items; maximum revenue: $9,111,110 
D)  10,250 items; maximum revenue: $2,157,895 
A)  5481 items; maximum revenue: $2,740,370 
B)  7481 items; maximum revenue: $2,586,033 
C)  20,500 items; maximum revenue: $9,111,110 
D)  10,250 items; maximum revenue: $2,157,895

Question 6

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 7

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 asymototes 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 asymotote of   ?

Accepted Answer

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

Question 8

Find the slant asymptote and graph the function and its asymptote on the same axes.

Accepted Answer

The answer of Find the slant asymptote and graph the...

Question 9

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

Accepted Answer

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

Question 10

Find the x-coordinates of all extrema and sketch the graph of   showing global and local behavior.

Accepted Answer

The answer of Find the x-coordinates of all extrema and...

Question 11

Sand is pouring from a pipe at the rate of 12 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)  0.21 ft/sec 
B)  0.07 ft/sec 
C)  0.25 ft/sec 
D)  0.03 ft/sec 
A)  0.21 ft/sec 
B)  0.07 ft/sec 
C)  0.25 ft/sec 
D)  0.03 ft/sec

Question 12

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 13

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

Accepted Answer

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

Question 14

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 15

A plane is located at   miles (horizontally) away from an airport at an altitude of 3 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 16

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

Accepted Answer

A)  0.306232 
B)  0.216232 
C)  0.136232 
D)  0.219565 
A)  0.306232 
B)  0.216232 
C)  0.136232 
D)  0.219565

Question 17

Find all asymptotes and extrema and sketch a graph.

Accepted Answer

vertical asymptotes:

Question 18

Determine the intervals where   is concave up and concave down.

Accepted Answer

A)  concave down for   concave up for   
B)  concave down for   concave up for   
C)  concave down for   cancave up for   
D)  concave down for   and   concave up for   
A)  concave down for   concave up for   
B)  concave down for   concave up for   
C)  concave down for   cancave up for   
D)  concave down for   and   concave up for

Question 19

The power required for a particular bird to fly at a speed   is proportional to   Find   to minimize the power.

Accepted Answer

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

Question 20

Graph the function and completely discuss the graph.

Accepted Answer

domain: @#IMG-DLM& vertical asymptotes:

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

A point moves on the graph of the equation so that the x-coordinate changes at a rate of 2 units per second. How fast is the y-coordinate changing at the point

Determine all significant features and sketch a graph.

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

A company's revenue for selling x (thousand) items is given by in millions of dollars. Find the value of x (rounded to the nearest item) that maximizes the revenue and find the maximum revenue (rounded to the nearest dollar).

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

Find the slant asymptote and graph the function and its asymptote on the same axes.

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

Find the x-coordinates of all extrema and sketch the graph of showing global and local behavior.

Sand is pouring from a pipe at the rate of 12 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 determine if the critical number represents a local maximum, local minimum or neither.

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

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

A plane is located at miles (horizontally) away from an airport at an altitude of 3 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?

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

Find all asymptotes and extrema and sketch a graph.

Determine the intervals where is concave up and concave down.

The power required for a particular bird to fly at a speed is proportional to Find to minimize the power.

Graph the function and completely discuss the graph.

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

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

A point moves on the graph of the equation so that the x-coordinate changes at a rate of 2 units per second. How fast is the y-coordinate changing at the point

Determine all significant features and sketch a graph.

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

A company's revenue for selling x (thousand) items is given by in millions of dollars. Find the value of x (rounded to the nearest item) that maximizes the revenue and find the maximum revenue (rounded to the nearest dollar).

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

Find the slant asymptote and graph the function and its asymptote on the same axes.

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

Find the x-coordinates of all extrema and sketch the graph of showing global and local behavior.

Sand is pouring from a pipe at the rate of 12 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 determine if the critical number represents a local maximum, local minimum or neither.

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

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

A plane is located at miles (horizontally) away from an airport at an altitude of 3 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?

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

Find all asymptotes and extrema and sketch a graph.

Determine the intervals where is concave up and concave down.

The power required for a particular bird to fly at a speed is proportional to Find to minimize the power.

Graph the function and completely discuss the graph.

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