Question 1

Find the limit, if it exists.
-Find

Accepted Answer

A)    
B)  0 
C)  2 
D)    
A)    
B)  0 
C)  2 
D)

Question 2

Solve the problem.
-Find the approximate number of batches (to the nearest whole number) of an item that should be produced annually if 280,000 units are to be made. It costs $2 to store a unit for one year, and it costs $460 to set up the
Factory to produce each batch.

Accepted Answer

A)  27 batches 
B)  18 batches 
C)  25 batches 
D)  20 batches 
A)  27 batches 
B)  18 batches 
C)  25 batches 
D)  20 batches

Question 3

Sketch a graph of a single function that has these properties.
-a) Continuous for all real numbers
b) Differentiable everywhere except x = 0
c)   d)   e)   f) f(-2) = f (2) = 5
g) y-intercept and x-intercept at (0, 0)

Accepted Answer

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

Question 4

Provide an appropriate response.
-Write the sign chart that corresponds to the following graph of f(x)::

Accepted Answer

The answer of Provide an appropriate response.
-Write the sign chart...

Question 5

Provide an appropriate response.
-Use the first derivative test to determine the local extrema, if any, for the function:

Accepted Answer

A)  f(x) has a local maximum at x = 4. 
B)  f(x) has a local minimum at x = 4. 
C)  f(x) has no local extrema 
D)  f(x) has a local minimum at 6 
A)  f(x) has a local maximum at x = 4. 
B)  f(x) has a local minimum at x = 4. 
C)  f(x) has no local extrema 
D)  f(x) has a local minimum at 6

Question 6

Find the intervals where the function has the indicated concavity. Give the x coordinates of inflection points.
-Concave downward

Accepted Answer

A)    
B)    
C)  (-1, 0); no inflection points 
D)    
A)    
B)    
C)  (-1, 0); no inflection points 
D)

Question 7

Provide an appropriate response.
-Find the absolute maximum value of   Round your answer to four decimal places.

Accepted Answer

The answer of Provide an appropriate response.
-Find the absolute maximum...

Question 8

Sketch the graph and show all local extrema and inflection points.
-

Accepted Answer

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

Question 9

Provide an appropriate response.
-The critical values of   are x = -2 and x = 2. Use the first derivative test to determine which of the critical values correspond to a local minimum.

Accepted Answer

A)  x = 2 and x = -2 
B)  neither x = 2 nor x = -2 correspond to a local minimum 
C)  x = -2 
D)  x = 2 
A)  x = 2 and x = -2 
B)  neither x = 2 nor x = -2 correspond to a local minimum 
C)  x = -2 
D)  x = 2

Question 10

Sketch a graph of a single function that has these properties.
-Find all inflection points for

Accepted Answer

A)    
B)  Inflection points at x = 1, x = 4 
C)  Inflection points at x = 0, x = 1, x = 4 
D)  This function does not have any inflection points. 
A)    
B)  Inflection points at x = 1, x = 4 
C)  Inflection points at x = 0, x = 1, x = 4 
D)  This function does not have any inflection points.

Question 11

Find the limit, if it exists.
-

Accepted Answer

A)  -3 
B)    
C)  3 
D)    
A)  -3 
B)    
C)  3 
D)

Question 12

Provide an appropriate response.
-Find the critical values and determine the intervals where f(x) is increasing and f(x) is decreasing if

Accepted Answer

A)    decreasing on   
B)    
C)    
D)    
A)    decreasing on   
B)    
C)    
D)

Question 13

Solve the problem.
-The annual revenue and cost functions for a manufacturer of grandfather clocks are approximately   where x denotes the number of clocks made. What is the maximum annual profit?

Accepted Answer

A)  $553,333 
B)  $753,333 
C)  $653,333 
D)  $853,333 
A)  $553,333 
B)  $753,333 
C)  $653,333 
D)  $853,333

Question 14

Solve the problem.
-The cost of manufacturing x electric woks in one day is given by C(x) = 2x3 -16x2 + 4x. Find the average cost per electric wok and the interval where the average cost per electric wok is decreasing.

Accepted Answer

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

Question 15

Provide an appropriate response.
-Find the absolute minimum value of   .

Accepted Answer

A)  min f(x) = f(2) = 21 
B)  min f(x) = f(1) = 25 
C)  min f(x) = f(2) = 13 
D)  min f(x) = f(0) = 5 
A)  min f(x) = f(2) = 21 
B)  min f(x) = f(1) = 25 
C)  min f(x) = f(2) = 13 
D)  min f(x) = f(0) = 5

Question 16

Provide an appropriate response.
-Find the absolute minimum value of f

Accepted Answer

A)  Absolute maximum is 6 at x = 3. 
B)  Absolute minimum is 3 at x = 6. 
C)  Absolute maximum is 3 at x = 6. 
D)  Absolute minimum is 6 at x = 3. 
A)  Absolute maximum is 6 at x = 3. 
B)  Absolute minimum is 3 at x = 6. 
C)  Absolute maximum is 3 at x = 6. 
D)  Absolute minimum is 6 at x = 3.

Find the limit, if it exists. -Find

Solve the problem. -Find the approximate number of batches (to the nearest whole number) of an item that should be produced annually if 280,000 units are to be made. It costs $2 to store a unit for one year, and it costs $460 to set up the Factory to produce each batch.

Sketch a graph of a single function that has these properties. -a) Continuous for all real numbers b) Differentiable everywhere except x = 0 c) d) e) f) f(-2) = f (2) = 5 g) y-intercept and x-intercept at (0, 0)

Provide an appropriate response. -Write the sign chart that corresponds to the following graph of f(x)::

Provide an appropriate response. -Use the first derivative test to determine the local extrema, if any, for the function:

Find the intervals where the function has the indicated concavity. Give the x coordinates of inflection points. -Concave downward

Provide an appropriate response. -Find the absolute maximum value of Round your answer to four decimal places.

Sketch the graph and show all local extrema and inflection points. -

Provide an appropriate response. -The critical values of are x = -2 and x = 2. Use the first derivative test to determine which of the critical values correspond to a local minimum.

Sketch a graph of a single function that has these properties. -Find all inflection points for

Find the limit, if it exists. -

Provide an appropriate response. -Find the critical values and determine the intervals where f(x) is increasing and f(x) is decreasing if

Solve the problem. -The annual revenue and cost functions for a manufacturer of grandfather clocks are approximately where x denotes the number of clocks made. What is the maximum annual profit?

Solve the problem. -The cost of manufacturing x electric woks in one day is given by C(x) = 2x3 -16x2 + 4x. Find the average cost per electric wok and the interval where the average cost per electric wok is decreasing.

Provide an appropriate response. -Find the absolute minimum value of .

Provide an appropriate response. -Find the absolute minimum value of f

Functions and Graphs

Limits and the Derivative

Additional Derivative Topics

Integration

Additional Integration Topics

Multivariable Calculus

Trigonometric Functions

Differential Equations

Taylor Polynomials and Infinite Series

Probability and Calculus

Basic Algebra Review

Special Topics

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Exam 4: Graphing and Optimization