Question 1

Provide an appropriate response.
-Find two numbers whose difference is 14 and whose product is a minimum.

Accepted Answer

A)  7 and -7 
B)  0 and 14 
C)  1 and 15 
D)  28 and 14 
A)  7 and -7 
B)  0 and 14 
C)  1 and 15 
D)  28 and 14

Question 2

Sketch a graph of a single function that has these properties.
-Find

Accepted Answer

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

Question 3

Provide an appropriate response.
-Find the absolute minimum value of f   . Round your answer to three decimal places.

Accepted Answer

A)  2.718 at x = 1 
B)  3 at x = 0.7439 
C)  0.7439 at x = 3 
D)  1 at x = 2.718 
A)  2.718 at x = 1 
B)  3 at x = 0.7439 
C)  0.7439 at x = 3 
D)  1 at x = 2.718

Question 4

Find the limit, if it exists.
-Find

Accepted Answer

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

Question 5

Provide an appropriate response.
-Find the absolute maximum and minimum values of the function   on the interval [-3, 0].

Accepted Answer

A)  Absolute minimum is 0 at x = 0. Absolute maximum is - 2 at x = -1. 
B)  Absolute maximum is 0 at x = 0. Absolute minimum is 2 at x = -1. 
C)  Absolute minimum is 0 at x = -1. Absolute maximum is - 2 at x = 0. 
D)  Absolute maximum is 0 at x = 0. Absolute minimum is -2 at x = -1. 
A)  Absolute minimum is 0 at x = 0. Absolute maximum is - 2 at x = -1. 
B)  Absolute maximum is 0 at x = 0. Absolute minimum is 2 at x = -1. 
C)  Absolute minimum is 0 at x = -1. Absolute maximum is - 2 at x = 0. 
D)  Absolute maximum is 0 at x = 0. Absolute minimum is -2 at x = -1.

Question 6

Sketch a graph of a single function that has these properties.
-a) Continuous and differentiable for all real numbers
b)   
c)   ) and ( -1 , 2)
d)   
e)   
f)   
g)

Accepted Answer

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

Question 7

Provide an appropriate response.
-Consider the function   Determine the intervals where f(x) is increasing and decreasing,
concave up and concave down and all local extrema. Use that information to obtain a sketch of the function.

Accepted Answer

f(x) is increasing on @#IMG-DLM& decreas

Question 8

Sketch a graph of the function.
-

Accepted Answer

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

Question 9

The graphs of the first and second derivatives of a function y = f(x) are given. Select a possible graph of f that passes
through the point P. (NOTE: Vertical scales may vary from graph to graph.)
-

Accepted Answer

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

Question 10

Provide an appropriate response.
-Find the relative extrema of the function. List your answer(s) in terms of ordered pair(s).

Accepted Answer

A)  No relative extrema 
B)  Relative maximum: (0, -8) 
C)  Relative maximum: (0, 8) 
D)  Relative maximum: (-1, 8) 
A)  No relative extrema 
B)  Relative maximum: (0, -8) 
C)  Relative maximum: (0, 8) 
D)  Relative maximum: (-1, 8)

Question 11

Provide an appropriate response.
-Determine the intervals for which the function   is decreasing.

Accepted Answer

A)    
B)  (0, 12) and (12, ∞) 
C)  (-12, 0) 
D)    
A)    
B)  (0, 12) and (12, ∞) 
C)  (-12, 0) 
D)

Question 12

Sketch a graph of the function.
-

Accepted Answer

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

Question 13

Solve the problem.
-A company manufactures and sells x pocket calculators per week. If the weekly cost and demand equations are given by:   Find the production level that maximizes profit.

Accepted Answer

A)  18,000 pocket calculators per week 
B)  8000 pocket calculators per week 
C)  2000 pocket calculators per week 
D)  14,000 pocket calculators per week 
A)  18,000 pocket calculators per week 
B)  8000 pocket calculators per week 
C)  2000 pocket calculators per week 
D)  14,000 pocket calculators per week

Question 14

Provide an appropriate response.
-Sketch the graph of   Include sketch of all asymptotes.

Accepted Answer

The answer of Provide an appropriate response.
-Sketch the graph of...

Question 15

Provide an appropriate response.
-Sketch the graph of   Include sketch of all asymptotes.

Accepted Answer

The answer of Provide an appropriate response.
-Sketch the graph of...

Question 16

Solve the problem.
-A logo baseball cap manufacturer has a uniform annual demand of 25,000 caps. It costs $1 to store one baseball
cap for 1 year and $500 to set up the plant for production of the logo baseball caps. How many times a year
should the company produce the caps in order to minimize the total storage and set-up costs? (Assume that
there are 250 working days per year.)

Accepted Answer

The company will min

Question 17

Provide an appropriate response.
-Find the relative extrema of the function. List your answer(s) in terms of ordered pair(s).

Accepted Answer

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

Question 18

Solve the problem.
-Because of material shortages, it is increasingly expensive to produce 6.2L diesel engines. In fact, the profit in millions of dollars from producing x hundred thousand engines is approximated by   Find the inflection point of this function to determine the point of
Diminishing returns.

Accepted Answer

A)  (7.50, 2048) 
B)  (10, 1958) 
C)  (10, 2048) 
D)  (10, 114.67) 
A)  (7.50, 2048) 
B)  (10, 1958) 
C)  (10, 2048) 
D)  (10, 114.67)

Question 19

Find the intervals where f''(x)  0 as indicated.
-

Accepted Answer

A)  (-3, 3) 
B)    
C)    
D)  (0, 3) 
A)  (-3, 3) 
B)    
C)    
D)  (0, 3)

Question 20

Provide an appropriate response.
-The percent of concentration of a acid absorbed in a new manufacturing process after x hr after the acid has been mixed is given by   How long after the acid has been added is the concentration a maximum?
Round answer to the nearest tenth, if necessary.

Accepted Answer

A)  2.5 hr 
B)  4.9 hr 
C)  4 hr 
D)  7 hr 
A)  2.5 hr 
B)  4.9 hr 
C)  4 hr 
D)  7 hr

Provide an appropriate response. -Find two numbers whose difference is 14 and whose product is a minimum.

Sketch a graph of a single function that has these properties. -Find

Provide an appropriate response. -Find the absolute minimum value of f . Round your answer to three decimal places.

Find the limit, if it exists. -Find

Provide an appropriate response. -Find the absolute maximum and minimum values of the function on the interval [-3, 0].

Sketch a graph of a single function that has these properties. -a) Continuous and differentiable for all real numbers b) c) ) and ( -1 , 2) d) e) f) g)

Provide an appropriate response. -Consider the function Determine the intervals where f(x) is increasing and decreasing, concave up and concave down and all local extrema. Use that information to obtain a sketch of the function.

Sketch a graph of the function. -

The graphs of the first and second derivatives of a function y = f(x) are given. Select a possible graph of f that passes through the point P. (NOTE: Vertical scales may vary from graph to graph.) -

Provide an appropriate response. -Find the relative extrema of the function. List your answer(s) in terms of ordered pair(s).

Provide an appropriate response. -Determine the intervals for which the function is decreasing.

Sketch a graph of the function. -

Solve the problem. -A company manufactures and sells x pocket calculators per week. If the weekly cost and demand equations are given by: Find the production level that maximizes profit.

Provide an appropriate response. -Sketch the graph of Include sketch of all asymptotes.

Provide an appropriate response. -Sketch the graph of Include sketch of all asymptotes.

Provide an appropriate response. -Find the relative extrema of the function. List your answer(s) in terms of ordered pair(s).

Find the intervals where f''(x) < 0 ir f''(x) > 0 as indicated. -

Provide an appropriate response. -The percent of concentration of a acid absorbed in a new manufacturing process after x hr after the acid has been mixed is given by How long after the acid has been added is the concentration a maximum? Round answer to the nearest tenth, if necessary.

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

Filters

Exam 4: Graphing and Optimization

Provide an appropriate response. -Find two numbers whose difference is 14 and whose product is a minimum.

Sketch a graph of a single function that has these properties. -Find

Provide an appropriate response. -Find the absolute minimum value of f . Round your answer to three decimal places.

Find the limit, if it exists. -Find

Provide an appropriate response. -Find the absolute maximum and minimum values of the function on the interval [-3, 0].

Sketch a graph of a single function that has these properties. -a) Continuous and differentiable for all real numbers b) c) ) and ( -1 , 2) d) e) f) g)

Provide an appropriate response. -Consider the function Determine the intervals where f(x) is increasing and decreasing, concave up and concave down and all local extrema. Use that information to obtain a sketch of the function.

Sketch a graph of the function. -

The graphs of the first and second derivatives of a function y = f(x) are given. Select a possible graph of f that passes through the point P. (NOTE: Vertical scales may vary from graph to graph.) -

Provide an appropriate response. -Find the relative extrema of the function. List your answer(s) in terms of ordered pair(s).

Provide an appropriate response. -Determine the intervals for which the function is decreasing.

Sketch a graph of the function. -

Solve the problem. -A company manufactures and sells x pocket calculators per week. If the weekly cost and demand equations are given by: Find the production level that maximizes profit.

Provide an appropriate response. -Sketch the graph of Include sketch of all asymptotes.

Provide an appropriate response. -Sketch the graph of Include sketch of all asymptotes.

Provide an appropriate response. -Find the relative extrema of the function. List your answer(s) in terms of ordered pair(s).

Find the intervals where f''(x) < 0 ir f''(x) > 0 as indicated. -

Provide an appropriate response. -The percent of concentration of a acid absorbed in a new manufacturing process after x hr after the acid has been mixed is given by How long after the acid has been added is the concentration a maximum? Round answer to the nearest tenth, if necessary.

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

Filters