Calculus and Its Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Bittinger, Ellenbogen & Surgent, The Calculus and Its Applications Series)
11th Edition
ISBN: 9780133795561
Author: Marvin L. Bittinger, David J. Ellenbogen, Scott J. Surgent
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Videos
Question
Chapter 6.5, Problem 2E
To determine
To calculate: The extremum of
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Please send me the answer for this question in clear way.
Please answer this question for me, make it in clear steps.
Please solve this question for me, make sure that the answer is in clear steps.
Chapter 6 Solutions
Calculus and Its Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Bittinger, Ellenbogen & Surgent, The Calculus and Its Applications Series)
Ch. 6.1 - Forf(x,y)=x23xy,find(0,2),f(2,3),andf(10,5).Ch. 6.1 - 2. .
Ch. 6.1 - 3. .
Ch. 6.1 - 4. .
Ch. 6.1 - Forf(x,y)=Inx+y3,findf(e,2),f(e2,4),andf(e3,5).Ch. 6.1 - 6. .
Ch. 6.1 - Forf(x,y,z)=x2y2+z2,findf(1,2,3)andf(2,1,3).Ch. 6.1 - 8. .
Ch. 6.1 - In Exercises 9-14, determine the domain of each...Ch. 6.1 - In Exercises 9-14, determine the domain of each...
Ch. 6.1 - In Exercises 9-14, determine the domain of each...Ch. 6.1 - In Exercises 9-14, determine the domain of each...Ch. 6.1 - In Exercises 9-14, determine the domain of each...Ch. 6.1 - In Exercises 9-14, determine the domain of each...Ch. 6.1 - 15. Price-earnings ratio. The price-earnings ratio...Ch. 6.1 - Yield. The yield of a stock is given by Y(D,P)=DP,...Ch. 6.1 - 17. Cost of storage equipment. Consider the cost...Ch. 6.1 - Savings and interest. A sum of $1000 is deposited...Ch. 6.1 - Monthly car payments. Ashley wants to buy a 2014...Ch. 6.1 - Prob. 20ECh. 6.1 - 21. Poiseuille’s Law. The speed of blood in a...Ch. 6.1 - Prob. 22ECh. 6.1 - 23. Body surface area. The Mosteller formula for...Ch. 6.1 - Body surface area. The Haycock formula for...Ch. 6.1 - 25. Goals against average. A hockey goalie’s goals...Ch. 6.1 - 26. Dewpoint. The dewpoint is the temperature at...Ch. 6.1 - For the tornado described in Exercise 22, if the...Ch. 6.1 - According to the Mosteller formula in Exercise 23,...Ch. 6.1 - Explain the difference between a function of two...Ch. 6.1 - 30. Find some examples of function of several...Ch. 6.1 - Wind Chill Temperature. Because wind speed...Ch. 6.1 - Wind Chill Temperature.
Because wind speed...Ch. 6.1 - Prob. 33ECh. 6.1 - Wind Chill Temperature.
Because wind speed...Ch. 6.1 - Use a 3D graphics program to generate the graph of...Ch. 6.1 - Use a 3D graphics program to generate the graph of...Ch. 6.1 - Use a 3D graphics program to generate the graph of...Ch. 6.1 - Use a 3D graphics program to generate the graph of...Ch. 6.1 - Prob. 40ECh. 6.1 - Use a 3D graphics program to generate the graph of...Ch. 6.2 - Find zx,zy,zx|(2,3),andzy|(0,5) z=7x5yCh. 6.2 - Find zx,zy,zx|(2,3),andzy|(0,5) z=2z3yCh. 6.2 - Prob. 3ECh. 6.2 - Find zx,zy,zx|(2,3),andzy|(0,5) z=2x3+3xyxCh. 6.2 - .
5.
Ch. 6.2 - .
6.
Ch. 6.2 - Find.
7.
Ch. 6.2 - Find fx,fy,fz(2,1),andfy(3,2). f(x,y)=x2y2Ch. 6.2 - Find
9.
Ch. 6.2 - Prob. 10ECh. 6.2 - Prob. 11ECh. 6.2 - Prob. 12ECh. 6.2 - Prob. 13ECh. 6.2 - Prob. 14ECh. 6.2 - Prob. 15ECh. 6.2 - Prob. 16ECh. 6.2 - Prob. 17ECh. 6.2 - Find fxandfy f(x,y)=xy+y5xCh. 6.2 - Prob. 19ECh. 6.2 - Find
20.
Ch. 6.2 - Find fbandfm f(b,m)=m3+4m2bb2+(2m+b5)2+(3m+b6)2Ch. 6.2 - Find fbandfm f(b,m)=5m2mb23b+(2m+b8)2+(3m+b9)2Ch. 6.2 - Find fx,fy,andf (The symbol is the Greek letter...Ch. 6.2 - Find (The symbol is the Greek letter...Ch. 6.2 - Find fx,fy,andf (The symbol is the Greek letter...Ch. 6.2 - Find fx,fy,andf (The symbol is the Greek letter...Ch. 6.2 - Prob. 27ECh. 6.2 - Prob. 28ECh. 6.2 - Find the four second-order partial derivatives....Ch. 6.2 - Find the four second-order partial derivatives....Ch. 6.2 - Prob. 31ECh. 6.2 - Prob. 32ECh. 6.2 - Find fxy,fxy,fyx,andfyy. (Remember, fyx means to...Ch. 6.2 - Find. (Remember, means to differentiate with...Ch. 6.2 - Find. (Remember, means to differentiate with...Ch. 6.2 - Find. (Remember, means to differentiate with...Ch. 6.2 - Find. (Remember, means to differentiate with...Ch. 6.2 - Find. (Remember, means to differentiate with...Ch. 6.2 - Find. (Remember, means to differentiate with...Ch. 6.2 - Find fxy,fxy,fyx,andfyy. (Remember, fyx means to...Ch. 6.2 - The Cobb-Douglas model. Riverside Appliances has...Ch. 6.2 - The Cobb-Douglas model. Lincolnville Sporting...Ch. 6.2 - A study of Texas nursing homes found that the...Ch. 6.2 - A study of Texas nursing homes found that the...Ch. 6.2 - Prob. 45ECh. 6.2 - Temperaturehumidity Heat Index. In summer, higher...Ch. 6.2 - Temperaturehumidity Heat Index. In summer, higher...Ch. 6.2 - Prob. 48ECh. 6.2 - Use the equation for Th given above for Exercises...Ch. 6.2 - Use the equation for Th given above for Exercises...Ch. 6.2 - Prob. 51ECh. 6.2 - Prob. 52ECh. 6.2 - Reading Ease
The following formula is used by...Ch. 6.2 - Reading Ease
The following formula is used by...Ch. 6.2 - Prob. 55ECh. 6.2 - Reading Ease The following formula is used by...Ch. 6.2 - Prob. 57ECh. 6.2 - Prob. 58ECh. 6.2 - Prob. 59ECh. 6.2 - Prob. 60ECh. 6.2 - Prob. 61ECh. 6.2 - Find fxandft. f(x,t)=(x2+t2x2t2)5Ch. 6.2 - In Exercises 63 and 64, find fxx,fxy,fyx,andfyy...Ch. 6.2 - In Exercises 63 and 64, find fxx,fxy,fyx,andfyy...Ch. 6.2 - Do some research on the Cobb-Douglas production...Ch. 6.2 - Prob. 66ECh. 6.2 - Considerf(x,y)=In(x2+y2). Show that f is a...Ch. 6.2 - Consider f(x,t)=x35xy2 Show that f is a solution...Ch. 6.2 - Prob. 69ECh. 6.3 - Find the relative maximum and minimum values. ...Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values. ...Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values. ...Ch. 6.3 - In Exercises 15-22, assume that relative maximum...Ch. 6.3 - In Exercises 15-22, assume that relative maximum...Ch. 6.3 - In Exercises 15-22, assume that relative maximum...Ch. 6.3 - In Exercises 15-22, assume that relative maximum...Ch. 6.3 - In Exercises 15-22, assume that relative maximum...Ch. 6.3 - In Exercises 15-22, assume that relative maximum...Ch. 6.3 - In Exercises 15-22, assume that relative maximum...Ch. 6.3 - In Exercises 15-22, assume that relative maximum...Ch. 6.3 - In Exercises 23-26, find the relative maximum and...Ch. 6.3 - In Exercises 23-26, find the relative maximum and...Ch. 6.3 - In Exercises 23-26, find the relative maximum and...Ch. 6.3 - In Exercises 23-26, find the relative maximum and...Ch. 6.3 - Is a cross-section of an anticlastic curve always...Ch. 6.3 - Explain the difference between a relative minimum...Ch. 6.3 - Use a 3D graphics program to graph each of the...Ch. 6.3 - Use a 3D graphics program to graph each of the...Ch. 6.3 - Use a 3D graphics program to graph each of the...Ch. 6.3 - Use a 3D graphics program to graph each of the...Ch. 6.4 - In Exercises 1 4, find the regression line for...Ch. 6.4 - In Exercises 1 – 4, find the regression line for...Ch. 6.4 - In Exercises 1 4, find the regression line for...Ch. 6.4 - In Exercises 1 – 4, find the regression line for...Ch. 6.4 - In Exercises 5-8, find an exponential regression...Ch. 6.4 - In Exercises 5-8, find an exponential regression...Ch. 6.4 - Prob. 7ECh. 6.4 - In Exercises 5-8, find an exponential regression...Ch. 6.4 - All of the following exercises can be done with a...Ch. 6.4 - All of the following exercises can be done with a...Ch. 6.4 - Prob. 11ECh. 6.4 - Prob. 12ECh. 6.4 - All of the following exercises can be done with a...Ch. 6.4 - All of the following exercises can be done with a...Ch. 6.4 - All of the following exercises can be done with a...Ch. 6.4 - All of the following exercises can be done with a...Ch. 6.4 - Prob. 17ECh. 6.4 - Prob. 18ECh. 6.5 - Find the extremum of f(x,y) subject to given...Ch. 6.5 - Prob. 2ECh. 6.5 - Prob. 3ECh. 6.5 - Prob. 4ECh. 6.5 - Find the extremum of f(x,y) subject to given...Ch. 6.5 - Find the extremum of f(x,y) subject to given...Ch. 6.5 - Find the extremum of f(x,y) subject to given...Ch. 6.5 - Find the extremum of subject to given constraint,...Ch. 6.5 - Find the extremum of f(x,y) subject to given...Ch. 6.5 - Find the extremum of subject to given constraint,...Ch. 6.5 - Prob. 11ECh. 6.5 - Prob. 12ECh. 6.5 - Prob. 13ECh. 6.5 - Prob. 14ECh. 6.5 - Prob. 15ECh. 6.5 - Prob. 16ECh. 6.5 - Prob. 17ECh. 6.5 - Prob. 18ECh. 6.5 - 19. Maximizing typing area. A standard piece of...Ch. 6.5 - 20. Maximizing room area. A carpenter is building...Ch. 6.5 - 21. Minimizing surface area. An oil drum of...Ch. 6.5 - Juice-can problem. A large juice can has a volume...Ch. 6.5 - Maximizing total sales. Total sales, S, of...Ch. 6.5 - Maximizing total sales. Total sales, S, of Sea...Ch. 6.5 - 25. Minimizing construction costs. Denney...Ch. 6.5 - Minimizing the costs of container construction....Ch. 6.5 - Minimizing total cost. Each unit of a product can...Ch. 6.5 - 28. Minimizing distance and cost. A highway passes...Ch. 6.5 - 29. Minimizing distance and cost. From the center...Ch. 6.5 -
In Exercises 30-33, find the absolute maximum and...Ch. 6.5 - In Exercises 30-33, find the absolute maximum and...Ch. 6.5 - In Exercises 30-33, find the absolute maximum and...Ch. 6.5 - In Exercises 30-33, find the absolute maximum and...Ch. 6.5 - Business: minimizing costs with constraints....Ch. 6.5 - Business: maximizing profits with constraints. A...Ch. 6.5 - Find the indicated maximum or minimum value of...Ch. 6.5 - Find the indicated maximum or minimum value of...Ch. 6.5 - Find the indicated maximum or minimum value of...Ch. 6.5 - Find the indicated maximum or minimum value of...Ch. 6.5 - Find the indicated maximum or minimum value of...Ch. 6.5 - Find the indicated maximum or minimum value of...Ch. 6.5 - Find the indicated maximum or minimum value of...Ch. 6.5 - Economics: the Law of Equimarginal Productivity....Ch. 6.5 - 44. Business: maximizing production. A computer...Ch. 6.5 - 45. Discuss the difference between solving...Ch. 6.5 - Write a brief report on the life and work of the...Ch. 6.5 - Prob. 47ECh. 6.6 - Prob. 1ECh. 6.6 - Prob. 2ECh. 6.6 - Prob. 3ECh. 6.6 - Prob. 4ECh. 6.6 - Evaluate. 4113(x+5y)dxdyCh. 6.6 - Prob. 6ECh. 6.6 - Prob. 7ECh. 6.6 - Evaluate.
8.
Ch. 6.6 - Evaluate. 01x2x(x+y)dydxCh. 6.6 - Prob. 10ECh. 6.6 - Prob. 11ECh. 6.6 - Evaluate.
12.
Ch. 6.6 - Evaluate. 020x(x+y2)dydxCh. 6.6 - Prob. 14ECh. 6.6 - Find the volume of the solid capped by the surface...Ch. 6.6 - 16. Find the volume of the solid capped by the...Ch. 6.6 - 17. Find the average value of.
Ch. 6.6 - 18. Find the average value of.
Ch. 6.6 - 19. Find the average value of, where the region of...Ch. 6.6 - Prob. 20ECh. 6.6 - 21. Life sciences: population. The population...Ch. 6.6 - 22. Life sciences: population. The population...Ch. 6.6 - Prob. 23ECh. 6.6 - Prob. 24ECh. 6.6 - Prob. 25ECh. 6.6 - Is evaluated in much the same way as a double...Ch. 6.6 - 27. Describe the geometric meaning of the double...Ch. 6.6 - 28. Explain how Exercise 1 can be answered without...Ch. 6.6 - Prob. 29ECh. 6.6 - Prob. 30ECh. 6.6 - Use a calculator that does multiple integration to...Ch. 6 - Match each expression in column A with an...Ch. 6 - Given f(x,y)=ey+3xy3+2y, find each of the...Ch. 6 - Given, find each of the following
10.
Ch. 6 - Given f(x,y)=ey+3xy3+2y, find each of the...Ch. 6 - Given, find each of the following
12.
Ch. 6 - Given, find each of the following
13.
Ch. 6 - Given f(x,y)=ey+3xy3+2y, find each of the...Ch. 6 - Given, find each of the following
15.
Ch. 6 - 16. State the domain of
Ch. 6 - Given, find each of the following
17.
Ch. 6 - Given z=2x3Iny+xy2, find each of the following...Ch. 6 - Given, find each of the following
19.
Ch. 6 - Given, find each of the following
20.
Ch. 6 - Given, find each of the following
21.
Ch. 6 - Given, find each of the following
22.
Ch. 6 - Find the relative maximum and minimum values [6.3]...Ch. 6 - Find the relative maximum and minimum values [6.3]...Ch. 6 - Find the relative maximum and minimum values [6.3]...Ch. 6 - Prob. 26RECh. 6 - 27. Consider the data in the following table...Ch. 6 - Consider the data in the table below regarding...Ch. 6 - 29. Find the extremum of Minimum
subject...Ch. 6 - Find the extremum of f(x,y)=6xy subject to the...Ch. 6 - Find the absolute maximum and minimum values of...Ch. 6 - Evaluate [6.6] 0112x2y3dydxCh. 6 - Evaluate
[6.6]
33.
Ch. 6 - Business: demographics. The density of students...Ch. 6 - 35. Evaluate
.
Ch. 6 - Prob. 36RECh. 6 - Prob. 37RECh. 6 - Prob. 38RECh. 6 - Given, find each of the following
1.
Ch. 6 - Prob. 2TCh. 6 - Given f(x,y)=ex+2x3y+y, find each of the following...Ch. 6 - Prob. 4TCh. 6 - Given, find each of the following
5.
Ch. 6 - Given, find each of the following
6.
Ch. 6 - Given f(x,y)=ex+2x3y+y, find each of the following...Ch. 6 - Find the relative maximum and minimum values....Ch. 6 - Prob. 9TCh. 6 - Prob. 10TCh. 6 - Prob. 11TCh. 6 - Prob. 12TCh. 6 - Prob. 13TCh. 6 - 14. Business: maximizing production. Southwest...Ch. 6 - Find fxandft: f(x,t)=x22tx3+2t.Ch. 6 - Use a 3D graphics program to graph...
Additional Math Textbook Solutions
Find more solutions based on key concepts
Disks/washers about the y-axis Let R be the region bounded by the following curves. Use the disk or washer meth...
Calculus: Early Transcendentals (2nd Edition)
Standard Normal Distribution. In Exercises 13–16, find the indicated z score. The graph depicts the standard no...
Elementary Statistics (13th Edition)
Time Employed A human resources manager for a large company takes a random sample of 50 employees from the comp...
Introductory Statistics
For years, telephone area codes in the United States and Canada consisted of a sequence of three digits. The fi...
A First Course in Probability (10th Edition)
Find T, N, and κ for the plane curves in Exercises 1–4.
3. r(t) = (2t + 3)i + (5 − t2)j
University Calculus: Early Transcendentals (4th Edition)
Identify f as being linear, quadratic, or neither. If f is quadratic, identify the leading coefficient a and ...
College Algebra with Modeling & Visualization (5th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- 48. f(x) = { 4 x if x < 2 2x 2 if x 2arrow_forwardГ 49. -x+1 if x 1 Answer ->arrow_forwardA Content X MindTap - Cengage Learning x Function Evaluations x + /ui/evo/index.html?elSBN=9780357038406&id=339416021&snapshotld=877369& GE MINDTAP , Limits, and the Derivative ⭑ វា a ANSWEI 16. Refer to the graph of the function f in the following figure. कर्ट AA C 54 -3-2 7 7 Ay 6. S 5. y=f(x) 4 3. 2. 1 -3- 34567 8 00 9 10 a. Find the value of ƒ (7). b. Find the values of x corresponding to the point(s) on the graph of ƒ located at a height of 5 units from the x-axis. c. Find the point on the x-axis at which the graph of ƒ crosses it. What is the value of f (x) at this point? d. Find the domain and range of f. MacBook Pro G Search or type URL + > % Λ & 5 6 7 29 ( 8 9 0arrow_forward
- Morgan F. - C X A Courses MindTap - Cengage Learning Х Domain of Square Roots X + gage.com/static/nb/ui/evo/index.html?elSBN 9780357038406&id=339416021&snapshotld=877369& CENGAGE MINDTAP 2: Functions, Limits, and the Derivative 47. x if x < 0 f(x) = 2x+1 if x 0 Answerarrow_forwardA Content MindTap - Cengage Learning × Function Evaluations * + c/nb/ui/evo/index.html?elSBN 9780357038406&id=339416021&snapshotld=877369& GAGE MINDTAP ions, Limits, and the Derivative 15. Refer to the graph of the function f in the following figure. 6 y = f(x) 5 4+ 3- 2- 1 + 2 -1 3 4 5 6 a. Find the value of ƒ (0). Answer-> b. Find the value of x for which (i) f (x) = 3 and (ii) f (x) = 0. Answer ▾ c. Find the domain of f. Answer + d. Find the range of f. Answer+ MacBook Proarrow_forwardAnswer-> 12. Let g be the function defined by Find g(-2), g(0), g (2), and g (4). - +1 if x <2 g(x) = √√√x-2 if x 2arrow_forward
- 13. Let f be the function defined by Find f (-1), f (0), ƒ (1) and ƒ (2). Answer f(x) = .2 J-x² +3 if x <1 2x²+1 2x²+1 if x ≥ 1arrow_forwardΛ Content Mind Tap - Cengage Learning × Function Evaluations x + c/nb/ui/evo/index.html?elSBN 9780357038406&id=339416021&snapshotld=877369& GAGE MINDTAP ons, Limits, and the Derivative 14. Let f be the function defined by Find f (0), f (1), and f (2). 2+1 x if x 1 if x 1 f(x) = 1 1-xarrow_forwardA Content c/nb/ui/evo/index.html?elSBN 9780357038406&id=339416021&snapshotld=877369& GAGE MINDTAP ons, Limits, and the Derivative 11. Let f be the function defined by Find f (-2), f (0), and f (1). Answer f(x) = [ x² + 1 if x ≤ 0 if x > 0arrow_forward
- Given that 4−4i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable. f(x)=x4−5x3−2x2+176x−320arrow_forwardeliminate the parameter to find the cartesian equation of the curve and sketch the graph. On the graph show the direction it takes and the initial and terminal point. Please draw by hand and show how you got to each steparrow_forwardeliminate the parameter to find the cartesian equation of the curve and sketch the graph. On the graph show the direction it takes and the initial and terminal point. Please draw by hand and show how you got to each steparrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Solve ANY Optimization Problem in 5 Steps w/ Examples. What are they and How do you solve them?; Author: Ace Tutors;https://www.youtube.com/watch?v=BfOSKc_sncg;License: Standard YouTube License, CC-BY
Types of solution in LPP|Basic|Multiple solution|Unbounded|Infeasible|GTU|Special case of LP problem; Author: Mechanical Engineering Management;https://www.youtube.com/watch?v=F-D2WICq8Sk;License: Standard YouTube License, CC-BY
Optimization Problems in Calculus; Author: Professor Dave Explains;https://www.youtube.com/watch?v=q1U6AmIa_uQ;License: Standard YouTube License, CC-BY
Introduction to Optimization; Author: Math with Dr. Claire;https://www.youtube.com/watch?v=YLzgYm2tN8E;License: Standard YouTube License, CC-BY