Question 1

Find the extreme values of the function and where they occur.
-y =

Accepted Answer

A)  Absolute maximum value is 1 at x = 0.5, absolute minimum value is -1 at x = 0.5. 
B)  Absolute maximum value is 1 at x = 0. 
C)  Absolute maximum value is 1 at x = 0.5. 
D)  Absolute minimum value is -1 at x = 0.5. 
A)  Absolute maximum value is 1 at x = 0.5, absolute minimum value is -1 at x = 0.5. 
B)  Absolute maximum value is 1 at x = 0. 
C)  Absolute maximum value is 1 at x = 0.5. 
D)  Absolute minimum value is -1 at x = 0.5.

Question 2

Find the linearization L(x) of f(x) at x = a.
-f(x) =   , a = 0

Accepted Answer

A)  L(x) = - 2/81 x + 1/81 
B)  L(x) = - 2/81 x + 1/9 
C)  L(x) = 2/81 x + 1/9 
D)  L(x) = 2/81 x + 1/81 
A)  L(x) = - 2/81 x + 1/81 
B)  L(x) = - 2/81 x + 1/9 
C)  L(x) = 2/81 x + 1/9 
D)  L(x) = 2/81 x + 1/81

Question 3

Use l'Hopital's Rule to evaluate the limit.
-  x sin

Accepted Answer

A)  0 
B)  1 
C)  4 
D)  1/4 
A)  0 
B)  1 
C)  4 
D)  1/4

Question 4

Use the graph of the function f(x) to locate the local extrema and identify the intervals where the function is concave up and concave down.   
-

Accepted Answer

A)  Local minimum at x = 0; local maximum at x = 2; concave up on (0, $\infty$); concave down on (-$\infty$, 0) 
B)  Local minimum at x = 0; local maximum at x = 2; concave down on (0, $\infty$); concave up on (-$\infty$, 0) 
C)  Local minimum at x = 2; local maximum at x = 0; concave down on (0, $\infty$); concave up on (-$\infty$, 0) 
D)  Local minimum at x = 2; local maximum at x = 0; concave up on (0, $\infty$); concave down on (-$\infty$, 0) 
A)  Local minimum at x = 0; local maximum at x = 2; concave up on (0, $\infty$); concave down on (-$\infty$, 0) 
B)  Local minimum at x = 0; local maximum at x = 2; concave down on (0, $\infty$); concave up on (-$\infty$, 0) 
C)  Local minimum at x = 2; local maximum at x = 0; concave down on (0, $\infty$); concave up on (-$\infty$, 0) 
D)  Local minimum at x = 2; local maximum at x = 0; concave up on (0, $\infty$); concave down on (-$\infty$, 0)

Question 5

Graph the equation. Include the coordinates of any local extreme points and inflection points.
-y =

Accepted Answer

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

Question 6

Find the largest open interval where the function is changing as requested.
-Decreasing f(x) =

Accepted Answer

A)  (-$\infty$, -4) 
B)  (4, $\infty$) 
C)  (-$\infty$, 4) 
D)  (-4, $\infty$) 
A)  (-$\infty$, -4) 
B)  (4, $\infty$) 
C)  (-$\infty$, 4) 
D)  (-4, $\infty$)

Question 7

Graph the equation. Include the coordinates of any local extreme points and inflection points.
-y =

Accepted Answer

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

Question 8

Provide an appropriate response.  
-Suppose the velocity of a body moving along the s-axis is      Find the body's displacement over the time interval from t=3  to  t=7 given that s=4  when  t=0

Accepted Answer

A)  180 
B)  212 
C)  39.2 
D)  4 
A)  180 
B)  212 
C)  39.2 
D)  4

Question 9

Find the most general antiderivative.      
-  dx

Accepted Answer

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

Question 10

L'Hopital's rule does not help with the given limit. Find the limit some other way.
-

Accepted Answer

A)  $\infty$ 
B)  1 
C)  -1 
D)  0 
A)  $\infty$ 
B)  1 
C)  -1 
D)  0

Question 11

Find the linearization L(x) of f(x) at x = a.
-f(x) =   , a = 0

Accepted Answer

A)  L(x) = 4/7 x - 7 
B)  L(x) = 2/7 x - 7 
C)  L(x) = 2/7 x + 7 
D)  L(x) = 4/7 x + 7 
A)  L(x) = 4/7 x - 7 
B)  L(x) = 2/7 x - 7 
C)  L(x) = 2/7 x + 7 
D)  L(x) = 4/7 x + 7

Question 12

Choose the one alternative that best completes the statement or answers the question. 
-A rectangular field is to be enclosed on four sides with a fence. Fencing costs $2 per foot for two opposite sides, and $7 per foot for the other two sides. Find the dimensions of the field of area 610 ft2 that would be the cheapest to enclose.

Accepted Answer

A)  13.2 ft @ $ 2 by 46.2 ft @ $ 7 
B)  7.1 ft @ $ 2 by 86.4 ft @ $ 7 
C)  86.4 ft @ $ 2 by 7.1 ft @ $ 7 
D)  46.2 ft @ $ 2 by 13.2 ft @ $ 7 
A)  13.2 ft @ $ 2 by 46.2 ft @ $ 7 
B)  7.1 ft @ $ 2 by 86.4 ft @ $ 7 
C)  86.4 ft @ $ 2 by 7.1 ft @ $ 7 
D)  46.2 ft @ $ 2 by 13.2 ft @ $ 7

Question 13

Find the limit.
-

Accepted Answer

A)  -4 
B)    
C)    
D)    
A)  -4 
B)    
C)    
D)

Question 14

Express the relationship between a small change in x and the corresponding change in y in the form   . 
-y = ln( 5 +   )

Accepted Answer

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

Question 15

For the given expression   , find y'' and sketch the general shape of the graph of y = f(x).
-y' = cos x, 0 $\le$ x $\le$ 2 $\pi$

Accepted Answer

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

Question 16

Sketch the graph and show all local extrema and inflection points.
-y = |   - 4x|

Accepted Answer

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

Question 17

Find the largest open interval where the function is changing as requested.
-Increasing f(x) = x2 - 2x + 1

Accepted Answer

A)  (0, $\infty$) 
B)  (1, $\infty$) 
C)  (-$\infty$, 1) 
D)  (-$\infty$, 0) 
A)  (0, $\infty$) 
B)  (1, $\infty$) 
C)  (-$\infty$, 1) 
D)  (-$\infty$, 0)

Question 18

Which of the graphs shows the solution of the given initial value problem?
-  = 2x, y = 2 when x = 1

Accepted Answer

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

Question 19

Choose the one alternative that best completes the statement or answers the question. 
-A trough is to be made with an end of the dimensions shown. The length of the trough is to be   long. Only the angle $\theta$can be varied. What value of $\theta$will maximize the trough's volume?

Accepted Answer

A)  30° 
B)  45° 
C)  32° 
D)  15° 
A)  30° 
B)  45° 
C)  32° 
D)  15°

Question 20

Choose the one alternative that best completes the statement or answers the question. 
-Suppose c(x) =   - 20   + 30,000x is the cost of manufacturing x items. Find a production level that will minimize the average cost of making x items.

Accepted Answer

A)  11 items 
B)  12 items 
C)  10 items 
D)  9 items 
A)  11 items 
B)  12 items 
C)  10 items 
D)  9 items

Find the extreme values of the function and where they occur. -y =

Find the linearization L(x) of f(x) at x = a. -f(x) = , a = 0

Use l'Hopital's Rule to evaluate the limit. - x sin

Use the graph of the function f(x) to locate the local extrema and identify the intervals where the function is concave up and concave down. -

Graph the equation. Include the coordinates of any local extreme points and inflection points. -y =

Find the largest open interval where the function is changing as requested. -Decreasing f(x) =

Graph the equation. Include the coordinates of any local extreme points and inflection points. -y =

Provide an appropriate response. -Suppose the velocity of a body moving along the s-axis is Find the body's displacement over the time interval from t=3 to t=7 given that s=4 when t=0

Find the most general antiderivative. - dx

L'Hopital's rule does not help with the given limit. Find the limit some other way. -

Find the linearization L(x) of f(x) at x = a. -f(x) = , a = 0

Find the limit. -

Express the relationship between a small change in x and the corresponding change in y in the form . -y = ln( 5 + )

Sketch the graph and show all local extrema and inflection points. -y = | - 4x|

Find the largest open interval where the function is changing as requested. -Increasing f(x) = x² - 2x + 1

Which of the graphs shows the solution of the given initial value problem? - = 2x, y = 2 when x = 1

Choose the one alternative that best completes the statement or answers the question. -Suppose c(x) = - 20 + 30,000x is the cost of manufacturing x items. Find a production level that will minimize the average cost of making x items.

Functions

Limits

Derivatives

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters

Exam 4: Applications of the Derivative

Find the extreme values of the function and where they occur. -y =

Find the linearization L(x) of f(x) at x = a. -f(x) = , a = 0

Use l'Hopital's Rule to evaluate the limit. - x sin

Use the graph of the function f(x) to locate the local extrema and identify the intervals where the function is concave up and concave down. -

Graph the equation. Include the coordinates of any local extreme points and inflection points. -y =

Find the largest open interval where the function is changing as requested. -Decreasing f(x) =

Graph the equation. Include the coordinates of any local extreme points and inflection points. -y =

Provide an appropriate response. -Suppose the velocity of a body moving along the s-axis is Find the body's displacement over the time interval from t=3 to t=7 given that s=4 when t=0

Find the most general antiderivative. - dx

L'Hopital's rule does not help with the given limit. Find the limit some other way. -

Find the linearization L(x) of f(x) at x = a. -f(x) = , a = 0

Find the limit. -

Express the relationship between a small change in x and the corresponding change in y in the form . -y = ln( 5 + )

For the given expression , find y'' and sketch the general shape of the graph of y = f(x). -y' = cos x, 0 ≤\le≤ x ≤\le≤ 2 π\piπ

Sketch the graph and show all local extrema and inflection points. -y = | - 4x|

Find the largest open interval where the function is changing as requested. -Increasing f(x) = x2 - 2x + 1

Which of the graphs shows the solution of the given initial value problem? - = 2x, y = 2 when x = 1

Choose the one alternative that best completes the statement or answers the question. -A trough is to be made with an end of the dimensions shown. The length of the trough is to be long. Only the angle θ\thetaθ can be varied. What value of θ\thetaθ will maximize the trough's volume?

Choose the one alternative that best completes the statement or answers the question. -Suppose c(x) = - 20 + 30,000x is the cost of manufacturing x items. Find a production level that will minimize the average cost of making x items.

Functions

Limits

Derivatives

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters

Find the largest open interval where the function is changing as requested. -Increasing f(x) = x² - 2x + 1