Mathematical Applications for the Management, Life, and Social Sciences
11th Edition
ISBN: 9781305108042
Author: Ronald J. Harshbarger, James J. Reynolds
Publisher: Cengage Learning
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Textbook Question
Chapter 1.6, Problem 10E
Given
What is the marginal profit, and what does it mean?
What should a firm with these cost, revenue, and profit functions do? (Hint: Graph the profit function and see where it goes.)
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Chapter 1 Solutions
Mathematical Applications for the Management, Life, and Social Sciences
Ch. 1.1 - 1. Solve the following for x.
(a)
(b)
(c)
Ch. 1.1 - 2. Solve for y:
Ch. 1.1 - Prob. 3CPCh. 1.1 - Prob. 4CPCh. 1.1 - Prob. 5CPCh. 1.1 -
In problems 1-16, solve each equation.
Solve
Ch. 1.1 - Prob. 2ECh. 1.1 - Prob. 3ECh. 1.1 - Prob. 4ECh. 1.1 - In problems 1-16, solve each equation.
5. Solve
Ch. 1.1 - Prob. 6ECh. 1.1 - In problems 1-16, solve each equation.
9. Solve
Ch. 1.1 - Prob. 8ECh. 1.1 - Prob. 9ECh. 1.1 - Prob. 10ECh. 1.1 - Prob. 11ECh. 1.1 - In problems 1-16, solve each equation.
14.
Ch. 1.1 - Prob. 13ECh. 1.1 - Prob. 14ECh. 1.1 - Prob. 15ECh. 1.1 - Prob. 16ECh. 1.1 - Prob. 17ECh. 1.1 - Prob. 18ECh. 1.1 - Prob. 19ECh. 1.1 - Prob. 20ECh. 1.1 - Prob. 21ECh. 1.1 - Prob. 22ECh. 1.1 - Prob. 23ECh. 1.1 - In Problems 23 – 26, use a calculator to solve...Ch. 1.1 - Prob. 25ECh. 1.1 - Prob. 26ECh. 1.1 - Prob. 27ECh. 1.1 - Prob. 28ECh. 1.1 - Prob. 29ECh. 1.1 - Prob. 30ECh. 1.1 - Prob. 31ECh. 1.1 - Prob. 32ECh. 1.1 - Prob. 33ECh. 1.1 - Prob. 34ECh. 1.1 - Prob. 35ECh. 1.1 - Prob. 36ECh. 1.1 - Prob. 37ECh. 1.1 - Prob. 38ECh. 1.1 - Prob. 39ECh. 1.1 - Prob. 40ECh. 1.1 - Prob. 41ECh. 1.1 - Prob. 42ECh. 1.1 - 45. Depreciation A $648,000 property is...Ch. 1.1 - 46. Depreciation When an $810,000 building is...Ch. 1.1 - 47. Credit card debt High interest rates make it...Ch. 1.1 - 48. Seawater pressure In seawater, the pressure p...Ch. 1.1 - Break-even Burnem, Inc. manufactures blank CDs and...Ch. 1.1 - 50. Break-even Dish systems manufactures satellite...Ch. 1.1 - 51. Profit In its second year of operation, a...Ch. 1.1 - 52. Sales Tax The total price of a used car...Ch. 1.1 - 56. Course grades Suppose a professor counts the...Ch. 1.1 - 58. Investment yields One safe investment pays 10%...Ch. 1.1 - 59. Salary increases A woman making $2000 per...Ch. 1.1 - 60. Wildlife management In wildlife management,...Ch. 1.1 - 61. Profit For a certain product, the revenue is...Ch. 1.1 - 62. Car Rental Thrift rents a compact car for $33...Ch. 1.1 - 63. Purchasing Sean can spend at most $900 for a...Ch. 1.1 - 64. Taxes In Sweetwater, Arizona, water bills are...Ch. 1.1 - Prob. 63ECh. 1.1 - Prob. 64ECh. 1.1 - Prob. 65ECh. 1.1 - 68. Wind chill The combination of cold...Ch. 1.2 - 1. If y = f(x), the independent variable is...Ch. 1.2 - Prob. 2CPCh. 1.2 - Prob. 3CPCh. 1.2 - Prob. 4CPCh. 1.2 - Prob. 5CPCh. 1.2 - Prob. 6CPCh. 1.2 - Prob. 1ECh. 1.2 - Prob. 2ECh. 1.2 - In Problems 3 and 4, are the relations defined by...Ch. 1.2 - Prob. 4ECh. 1.2 - Prob. 5ECh. 1.2 - Prob. 6ECh. 1.2 - Prob. 7ECh. 1.2 - Prob. 8ECh. 1.2 - Prob. 9ECh. 1.2 - Prob. 10ECh. 1.2 - Prob. 11ECh. 1.2 - Prob. 12ECh. 1.2 - 9. If , find the following.
(a) (b) (c) (d)
Ch. 1.2 - 10. If , find the following.
(a) (b) (c) (d)
Ch. 1.2 - 11. If , find the following.
(a) (b) (c) (d)...Ch. 1.2 - 12. If , find the following.
(a) (b) (c) (d)...Ch. 1.2 - 13. If , find the following.
(a) (b) (c) (d)...Ch. 1.2 - 14. If , find the following.
(a) (b) (c)...Ch. 1.2 - 15. If , find the following.
(a) (b) (c)
Ch. 1.2 - 16. If , find the following.
(a) (b) (c)
Ch. 1.2 - Prob. 21ECh. 1.2 - 18. Let and .
Does ?
Find .
Does
Does
Find and...Ch. 1.2 - Prob. 23ECh. 1.2 - 20. If and , find the following and simplify.
(a)...Ch. 1.2 - Prob. 25ECh. 1.2 - 22. Suppose y = g(x) has the graph in Problem...Ch. 1.2 - Prob. 27ECh. 1.2 - Prob. 28ECh. 1.2 - Prob. 29ECh. 1.2 - State the domain and range of each of the function...Ch. 1.2 - Prob. 31ECh. 1.2 - Prob. 32ECh. 1.2 - In Problems 29 – 32, a function and its graph are...Ch. 1.2 - Prob. 34ECh. 1.2 - Prob. 35ECh. 1.2 - Prob. 36ECh. 1.2 - Prob. 37ECh. 1.2 - For and given in the Problems 33 – 36, find
(a) ...Ch. 1.2 - Prob. 39ECh. 1.2 - Prob. 40ECh. 1.2 - For and given in the Problem 37 – 40, find
(a) ...Ch. 1.2 - For and given in the Problem 37 – 40, find
(a) ...Ch. 1.2 - For and given in the Problem 37 – 40, find
(a) ...Ch. 1.2 - Prob. 44ECh. 1.2 - Prob. 45ECh. 1.2 - 42. Debt refinancing When a debt is refinanced,...Ch. 1.2 - Prob. 47ECh. 1.2 - 44. Dow Jones Industrial Average The graph shows...Ch. 1.2 - Prob. 49ECh. 1.2 - Prob. 50ECh. 1.2 - 47. Temperature measurement The equation
gives...Ch. 1.2 - 48. Profit The profit from the production and sale...Ch. 1.2 - Prob. 53ECh. 1.2 - Prob. 54ECh. 1.2 - Prob. 55ECh. 1.2 - 52. Shipping restrictions If a box with a square...Ch. 1.2 - 53. Profit Suppose that the profit from the...Ch. 1.2 - 54. Fish species growth For many species of fish,...Ch. 1.2 - Prob. 59ECh. 1.2 - Prob. 60ECh. 1.2 - 57. Fencing a lot A farmer wants to fence the...Ch. 1.2 - 58. Cost A shipping crate has a square base with...Ch. 1.2 - 59. Revenue An agency charges $100 per person for...Ch. 1.2 - 60. Revenue A company handles an apartment...Ch. 1.3 - 1. Find the slope of the line throughand.
Ch. 1.3 - If a line has slope, then the line is. If a line...Ch. 1.3 - Prob. 3CPCh. 1.3 - Prob. 4CPCh. 1.3 - Prob. 5CPCh. 1.3 - Prob. 1ECh. 1.3 - Prob. 2ECh. 1.3 - Prob. 3ECh. 1.3 - Prob. 4ECh. 1.3 - Prob. 5ECh. 1.3 - Prob. 6ECh. 1.3 - Prob. 7ECh. 1.3 - Prob. 8ECh. 1.3 - Prob. 9ECh. 1.3 - Prob. 10ECh. 1.3 - Prob. 11ECh. 1.3 - Prob. 12ECh. 1.3 - 13. What is the rate of change of the function...Ch. 1.3 - 14. What is the rate of change of the function...Ch. 1.3 - Prob. 15ECh. 1.3 - Prob. 16ECh. 1.3 - Prob. 17ECh. 1.3 - In Problems 17-24, find the slope and y-intercept...Ch. 1.3 - In Problems 17-24, find the slope and y-intercept...Ch. 1.3 - Prob. 20ECh. 1.3 - Prob. 21ECh. 1.3 - Prob. 22ECh. 1.3 - In Problems 17-24, find the slope and y-intercept...Ch. 1.3 - Prob. 24ECh. 1.3 - In Problems 25-28, write the slope-intercept form...Ch. 1.3 - Prob. 26ECh. 1.3 - In Problems 25-28, write the slope-intercept form...Ch. 1.3 - In Problems 25-28, write the slope-intercept form...Ch. 1.3 - In Problems 29-34, write the equation of the line...Ch. 1.3 - In Problems 29-34, write the equation of the line...Ch. 1.3 - Prob. 31ECh. 1.3 - In Problems 29-34, write the equation of the line...Ch. 1.3 - In Problems 29-34, write the equation of the line...Ch. 1.3 - In Problems 29-34, write the equation of the line...Ch. 1.3 - In Problems 35-40, write the equation of each line...Ch. 1.3 - Prob. 36ECh. 1.3 - Prob. 37ECh. 1.3 - Prob. 38ECh. 1.3 - Prob. 39ECh. 1.3 - Prob. 40ECh. 1.3 - Prob. 41ECh. 1.3 - Prob. 42ECh. 1.3 - Prob. 43ECh. 1.3 - Prob. 44ECh. 1.3 - Prob. 45ECh. 1.3 - 46. Write the equation of the line passing...Ch. 1.3 - Prob. 47ECh. 1.3 - Prob. 48ECh. 1.3 - Prob. 49ECh. 1.3 - 50. U.S population Using Social Security...Ch. 1.3 - Internet users The percent of the U.S. population...Ch. 1.3 - 54. Temperature-humidity models Two models for...Ch. 1.3 - 56. Gross domestic product The U.S. gross domestic...Ch. 1.3 - 57. Residential electric costs An electric utility...Ch. 1.3 - 58. Residential heating costs Residential...Ch. 1.3 - 59. Civilian workforce The size of the U.S....Ch. 1.3 - 60. Pension plans According to USA Today most...Ch. 1.3 - 61. Consumer price index The projected consumer...Ch. 1.3 - 62. Drinking and driving The following table gives...Ch. 1.3 - 63. Population effects It has been estimated that...Ch. 1.3 - 64. Age-sleep relationship Each day, a young...Ch. 1.3 - 65. Insulation R-values The R-value of insulation...Ch. 1.3 - 66. Depreciation Suppose the cost of a business...Ch. 1.3 - Prob. 67ECh. 1.4 - Use a graphing calculator and the standard viewing...Ch. 1.4 - Prob. 2CPCh. 1.4 - Prob. 1ECh. 1.4 - Prob. 2ECh. 1.4 - Prob. 3ECh. 1.4 - Prob. 4ECh. 1.4 - Prob. 5ECh. 1.4 - Prob. 6ECh. 1.4 - Prob. 7ECh. 1.4 - Prob. 8ECh. 1.4 - Prob. 9ECh. 1.4 - Prob. 10ECh. 1.4 - Prob. 11ECh. 1.4 - Prob. 12ECh. 1.4 - Prob. 13ECh. 1.4 - Prob. 14ECh. 1.4 - Prob. 15ECh. 1.4 - Prob. 16ECh. 1.4 - Prob. 17ECh. 1.4 - Prob. 18ECh. 1.4 - Prob. 19ECh. 1.4 - Prob. 20ECh. 1.4 - Prob. 21ECh. 1.4 - Prob. 22ECh. 1.4 - Prob. 23ECh. 1.4 - Prob. 24ECh. 1.4 - Prob. 25ECh. 1.4 - Prob. 26ECh. 1.4 - Prob. 27ECh. 1.4 - Prob. 28ECh. 1.4 - Prob. 29ECh. 1.4 - Prob. 30ECh. 1.4 - Prob. 31ECh. 1.4 - Prob. 32ECh. 1.4 - Prob. 33ECh. 1.4 - Prob. 34ECh. 1.4 - Prob. 35ECh. 1.4 - Prob. 36ECh. 1.4 - Prob. 37ECh. 1.4 - In Problems 35-38, use the x-intercept method to...Ch. 1.4 - Prob. 39ECh. 1.4 - Prob. 40ECh. 1.4 - Consumer expenditure Suppose that the consumer...Ch. 1.4 - Prob. 44ECh. 1.4 - Prob. 45ECh. 1.4 - Learning rate In a study using foreign language...Ch. 1.4 - Elderly men in the workforce Using data from 1920...Ch. 1.4 - Prob. 48ECh. 1.4 - Prob. 49ECh. 1.4 - Pollution Suppose the cost C of removing p...Ch. 1.4 - Prob. 51ECh. 1.4 - Prob. 52ECh. 1.5 - Solve by substitution:
Ch. 1.5 - Prob. 2CPCh. 1.5 - Prob. 3CPCh. 1.5 - Prob. 4CPCh. 1.5 - Prob. 1ECh. 1.5 - Prob. 2ECh. 1.5 - Prob. 3ECh. 1.5 - Prob. 4ECh. 1.5 - Prob. 5ECh. 1.5 - Prob. 6ECh. 1.5 - Prob. 7ECh. 1.5 - Prob. 8ECh. 1.5 - In Problems 7-10, solve the systems of equations...Ch. 1.5 - Prob. 10ECh. 1.5 - In Problems 7-10, solve the systems of equations...Ch. 1.5 - In Problems 7-10, solve the systems of equations...Ch. 1.5 - Prob. 13ECh. 1.5 - In Problems 11-22, solve each system by...Ch. 1.5 - Prob. 15ECh. 1.5 - In Problems 11-22, solve each system by...Ch. 1.5 - Prob. 17ECh. 1.5 - Prob. 18ECh. 1.5 - Prob. 19ECh. 1.5 - In Problems 11-22, solve each system by...Ch. 1.5 - In Problems 11-22, solve each system by...Ch. 1.5 - Prob. 22ECh. 1.5 - In Problems 11-22, solve each system by...Ch. 1.5 - Prob. 24ECh. 1.5 - Use a graphing calculator or Excel to find the...Ch. 1.5 - Prob. 26ECh. 1.5 - Prob. 27ECh. 1.5 - Prob. 28ECh. 1.5 - Prob. 29ECh. 1.5 - Use the left-to right elimination method to solve...Ch. 1.5 - Prob. 31ECh. 1.5 - Prob. 32ECh. 1.5 - Prob. 33ECh. 1.5 - Prob. 34ECh. 1.5 - Temperature and travelling When U.S citizens...Ch. 1.5 - Population distribution Using U.S Census Bureau...Ch. 1.5 - Pricing A concert promoter needs to make $42,000...Ch. 1.5 - Rental income A woman has $500,000 invested in two...Ch. 1.5 - Investment yields One safe investment pays 10% per...Ch. 1.5 - Loans A bank lent $237,000 to a company tor the...Ch. 1.5 - Rental income A woman has $470,000 invested in two...Ch. 1.5 - Loans Mr. Jackson borrowed money from his bank and...Ch. 1.5 - 41. Nutrition Each ounce of substance A supplies...Ch. 1.5 - 42. Nutrition A glass of skim milk supplies 0.1 mg...Ch. 1.5 - 43. Bacterial growth Bacteria of species A and...Ch. 1.5 - 44. Botany A biologist has a 40% solution and a...Ch. 1.5 - 45. Medications A nurse has two solutions that...Ch. 1.5 - 46. Medications Medication A is given every 4...Ch. 1.5 - 47. Pricing A concert promoter needs to take in...Ch. 1.5 - 48. Pricing A nut wholesaler sells a mix of...Ch. 1.5 - 49. Nutrient solutions How many cubic centimeters...Ch. 1.5 - 50. Mixtures How many gallons of washer fluid that...Ch. 1.5 - 51. Nutrition Each ounce of substance A supplies...Ch. 1.5 - Prob. 54ECh. 1.5 - 53. Social services A social agency is charged...Ch. 1.5 - Prob. 56ECh. 1.6 - Suppose that when a company produces its produces...Ch. 1.6 - Suppose the company in Problem 1 sells its product...Ch. 1.6 - (a) Give the formula for profit in terms of...Ch. 1.6 - Prob. 4CPCh. 1.6 - Prob. 5CPCh. 1.6 - Prob. 6CPCh. 1.6 - Suppose a calculator manufacturer has the total...Ch. 1.6 - Prob. 2ECh. 1.6 - Suppose a ceiling fan manufacturer has the total...Ch. 1.6 - Suppose a computer manufacturer has the total cost...Ch. 1.6 - TOTAL COST, TOTAL REVENUE, AND PROFIT A linear...Ch. 1.6 - TOTAL COST, TOTAL REVENUE, AND PROFIT A linear...Ch. 1.6 - A linear revenue function is.
What is the...Ch. 1.6 - A linear revenue function is.
What is the...Ch. 1.6 - Prob. 9ECh. 1.6 - Given and, find the profit function.
What is the...Ch. 1.6 - Prob. 11ECh. 1.6 - Prob. 12ECh. 1.6 - Extreme Protection Inc. manufactures helmets for...Ch. 1.6 - TOTAL COST, TOTAL REVENUE, AND PROFIT A...Ch. 1.6 - The figure shows graphs of the total cost function...Ch. 1.6 - A manufacturer of shower surrounds has a revenue...Ch. 1.6 - A jewelry maker incurs costs for a necklace...Ch. 1.6 - BREAK-EVEN ANALYSIS A small business recaps and...Ch. 1.6 - A manufacturer sells belts for $12 per unit. The...Ch. 1.6 - A manufacturer sells watches for $50 per unit. The...Ch. 1.6 - (a) Write the profit function for problem 19.
(b)...Ch. 1.6 - (a) Write the profit function for Problem 20.
(b)...Ch. 1.6 - 23.Electronic equipment manufacturer Dynamo...Ch. 1.6 - 24.Financial Paper Inc. is a printer of checks and...Ch. 1.6 - 25.A company manufactures and sells bookcases....Ch. 1.6 -
Ch. 1.6 - In Problem 27 and 28, some of the graphs of total...Ch. 1.6 - In Problem 27 and 28, some of the graphs of total...Ch. 1.6 - SUPPLY, DEMAND, AND MARKET EQUILIBRIUM As the...Ch. 1.6 - Prob. 30ECh. 1.6 - The graphs of the demand function and supply...Ch. 1.6 - The graphs of the demand function and supply...Ch. 1.6 - 33. If the demand for a pair of shoes is given by...Ch. 1.6 - 34. If the demand function and supply function...Ch. 1.6 - 35. Suppose a certain outlet chain selling...Ch. 1.6 - Suppose a certain home improvement outlet knows...Ch. 1.6 - Suppose the manufacturer of a custom board game...Ch. 1.6 - Suppose a mining company will supply 100,000 tons...Ch. 1.6 - Complete Problems 39-43 using the accompanying...Ch. 1.6 - (a) If the price is $30, what quantity is...Ch. 1.6 - (a) If the price is $20, what quantity is...Ch. 1.6 - Prob. 42ECh. 1.6 - Will a price below the equilibrium price result in...Ch. 1.6 - Find the market equilibrium point for the...Ch. 1.6 - Find the market equilibrium point for the...Ch. 1.6 - Find the equilibrium point for the following...Ch. 1.6 - Find the equilibrium point for the following...Ch. 1.6 - Retailers will buy 45 cordless phones from a...Ch. 1.6 - A group of retailers will buy 80 televisions from...Ch. 1.6 - Stutz Department store will buy 10 pairs of...Ch. 1.6 - Problems involve market equilibrium after a given...Ch. 1.6 - Problems involve market equilibrium after a given...Ch. 1.6 - Problems involve market equilibrium after a given...Ch. 1.6 - Prob. 54ECh. 1.6 - Problems involve market equilibrium after a given...Ch. 1.6 - Prob. 56ECh. 1.6 - Prob. 57ECh. 1.6 - Problems involve market equilibrium after a given...Ch. 1 - Solve the equations in Problems 1-6
Ch. 1 - Solve the equations in problem 1-6.
2.
Ch. 1 - Prob. 3RECh. 1 - Prob. 4RECh. 1 - Prob. 5RECh. 1 - Solve the equations in problems 1-6
6.
Ch. 1 - Prob. 7RECh. 1 - Prob. 8RECh. 1 - Prob. 9RECh. 1 - Prob. 10RECh. 1 - Prob. 11RECh. 1 - Prob. 12RECh. 1 - Prob. 13RECh. 1 - Prob. 14RECh. 1 - Prob. 15RECh. 1 - Prob. 16RECh. 1 - Prob. 17RECh. 1 - In Problem 18 and 19, determine whether each graph...Ch. 1 - Prob. 19RECh. 1 - Prob. 20RECh. 1 - Prob. 21RECh. 1 - Prob. 22RECh. 1 - Prob. 23RECh. 1 - Prob. 24RECh. 1 - Prob. 25RECh. 1 - Prob. 26RECh. 1 - Prob. 27RECh. 1 - Prob. 28RECh. 1 - Prob. 29RECh. 1 - Prob. 30RECh. 1 - Prob. 31RECh. 1 - Prob. 32RECh. 1 - Prob. 33RECh. 1 - In problems 31-38, write the equation of each line...Ch. 1 - Prob. 35RECh. 1 - Prob. 36RECh. 1 - Prob. 37RECh. 1 - Prob. 38RECh. 1 - Prob. 39RECh. 1 - Prob. 40RECh. 1 - Prob. 41RECh. 1 - Prob. 42RECh. 1 - Prob. 43RECh. 1 - In Problem 45-51, solve each system of...Ch. 1 - Prob. 45RECh. 1 - Prob. 46RECh. 1 - Prob. 47RECh. 1 - Prob. 48RECh. 1 - Prob. 49RECh. 1 - Prob. 50RECh. 1 - 52. Life expectancy at age 65 Using Social...Ch. 1 - 53. Course grades In a certain course, grades are...Ch. 1 - 54. Cost analysis The owner of a small...Ch. 1 - Prob. 54RECh. 1 - Prob. 55RECh. 1 - Prob. 56RECh. 1 - 58. Fish species growth For many species of fish,...Ch. 1 - Prob. 58RECh. 1 - Prob. 59RECh. 1 - Prob. 60RECh. 1 - Health care costs The average annual cost per...Ch. 1 - Prob. 62RECh. 1 - Prob. 63RECh. 1 - 65.Flow rates of water -The speed at which water...Ch. 1 - Prob. 65RECh. 1 - 67.Botany A botanist has a 20% solution and a 70%...Ch. 1 - Prob. 67RECh. 1 - Prob. 68RECh. 1 - Prob. 69RECh. 1 - Cost, revenue and profit A certain commodity sells...Ch. 1 - 72. Market analysis –The supply function and the...Ch. 1 - 73. Market analysis Suppose that for a certain...Ch. 1 - Prob. 1TCh. 1 - Prob. 2TCh. 1 - Prob. 3TCh. 1 - Prob. 4TCh. 1 - Prob. 5TCh. 1 - Prob. 6TCh. 1 - Prob. 7TCh. 1 - Prob. 8TCh. 1 - Prob. 9TCh. 1 - Prob. 10TCh. 1 - Prob. 11TCh. 1 - Prob. 12TCh. 1 - Prob. 13TCh. 1 - Prob. 14TCh. 1 - Prob. 15TCh. 1 - Prob. 16TCh. 1 - [Type here]
Using U.S. Bureau of Labor Statistics...Ch. 1 - Prob. 18TCh. 1 - The selling price for each item of a product is...Ch. 1 - The supply function for a product is p=5q+1500,...Ch. 1 - Prob. 21TCh. 1 - An airline has 360 seats on a plane for one of its...Ch. 1 - Amanda plans to invest $20,000, part of it at a 9...Ch. 1 - I. Hospital Administration
Southwest Hospital...Ch. 1 - I. Hospital Administration
Southwest Hospital...Ch. 1 - I. Hospital Administration
Southwest Hospital...Ch. 1 - I. Hospital Administration
Southwest Hospital...Ch. 1 - I. Hospital Administration
Southwest Hospital...Ch. 1 - Prob. 1EAGP2Ch. 1 - Prob. 2EAGP2Ch. 1 - Prob. 3EAGP2Ch. 1 - Prob. 4EAGP2
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Finding Local Maxima and Minima by Differentiation; Author: Professor Dave Explains;https://www.youtube.com/watch?v=pvLj1s7SOtk;License: Standard YouTube License, CC-BY