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Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
Publisher: Cengage Learning
ISBN: 9781337625340

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Chapter
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BuyFindarrow_forward

Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
Publisher: Cengage Learning
ISBN: 9781337625340
Chapter 11.3, Problem 48E
Textbook Problem
5 views

At what points does the curve defined by x 2 + 4 y 2 4 = 0 have

(a) horizontal tangents?

(b) vertical tangents?

(a)

To determine

To calculate: The point at which the curve defined by x2+4y24=0 has horizontal tangents.

Explanation of Solution

Given Information:

The provided equation of the curve is, x2+4y24=0.

Formula used:

The slope of tangent to a curve y=f(x) at point (x,y) is given by the derivative of the curve at that point.

The power rule of differentiation:

ddx(xn)=nxn1

Calculation:

Consider the provided equation of curve,

x2+4y24=0

Now, find the derivative dydx from x2+4y24=0 by taking the derivative term by term on both sides of the equation as,

ddx(x2)+ddx(4y2)ddx(4)=ddx(0)2x+8ydydx0

(b)

To determine

To calculate: The point at which the curve defined by x2+4y24=0 has vertical tangents.

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Chapter 11 Solutions

Mathematical Applications for the Management, Life, and Social Sciences
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Ch. 11.1 - Find the derivatives of the functions in Problems...Ch. 11.1 - Find the derivatives of the functions in Problems...Ch. 11.1 - Find the derivatives of the functions in Problems...Ch. 11.1 - Find the derivatives of the functions in Problems...Ch. 11.1 - 11. Find . Ch. 11.1 - 12. Find . Ch. 11.1 - In each of Problems 13-18, find the derivative of...Ch. 11.1 - In each of Problems 13-18, find the derivative of...Ch. 11.1 - In each of Problems 13-18, find the derivative of...Ch. 11.1 - In each of Problems 13-18, find the derivative of...Ch. 11.1 - In each of Problems 13-18, find the derivative of...Ch. 11.1 - In each of Problems 13-18, find the derivative of...Ch. 11.1 - 19. Find . Ch. 11.1 - 20. Find . Ch. 11.1 - 21. Find Ch. 11.1 - 22. Find Ch. 11.1 - 23. Find Ch. 11.1 - 24. Find Ch. 11.1 - In Problems 25-38, find y'. Ch. 11.1 - In Problems 25-38, find y'. 26. Ch. 11.1 - In Problems 25-38, find y'. 27. Ch. 11.1 - In Problems 25-38, find y'. 28. Ch. 11.1 - In Problems 25-38, find y'. 29. Ch. 11.1 - In Problems 25-38, find y'. 30. Ch. 11.1 - In Problems 25-38, find y'. 31. Ch. 11.1 - In Problems 25-38, find y'. 32. Ch. 11.1 - In Problems 25-38, find y'. 33. Ch. 11.1 - In Problems 25-38, find y'. 34. Ch. 11.1 - In Problems 25-38, find y'. 35. Ch. 11.1 - In Problems 25-38, find y'. 36. Ch. 11.1 - In Problems 25-38, find y'. 37. Ch. 11.1 - In Problems 25-38, find y'. 38. Ch. 11.1 - In Problems 39-42, find the relative maxima and...Ch. 11.1 - In Problems 39-42, find the relative maxima and...Ch. 11.1 - In Problems 39-42, find the relative maxima and...Ch. 11.1 - In Problems 39-42, find the relative maxima and...Ch. 11.1 - 43. Marginal cost Suppose that the total cost (in...Ch. 11.1 - 44. Investment If money is invested at the...Ch. 11.1 - 45. Marginal revenue The total revenue, in...Ch. 11.1 - 46. Supply Suppose that the supply of x units of a...Ch. 11.1 - 47. Demand The demand function for a product is...Ch. 11.1 - 48. pH level The pH of a solution is given...Ch. 11.1 - 49. Drug concentration Concentration (in mg/ml) in...Ch. 11.1 - 50. Decibels The loudness of sound (L, measured in...Ch. 11.1 - 51. Richter scale The Richter scale reading, R,...Ch. 11.1 - 52. Women in the workforce From 1950 and projected...Ch. 11.2 - 1. If , find y’. Ch. 11.2 - 2. If , find y’. Ch. 11.2 - 3. If find ds/dt. Ch. 11.2 - 4. If the sales of a product are given by , where...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - 35. 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The area of a circle is changing at a rate of...Ch. 11.4 - 15. The volume of a cube is increasing at a rate...Ch. 11.4 - 16. The lengths of the edges of a cube are...Ch. 11.4 - 17. Profit Suppose that the daily profit (in...Ch. 11.4 - 18. Profit Suppose that the monthly revenue and...Ch. 11.4 - 19. Demand Suppose that the price p (in dollars)...Ch. 11.4 - 20. Supply The supply function for a product is...Ch. 11.4 - 21. Capital investment and production Suppose that...Ch. 11.4 - 22. Boyle's law Boyles law for enclosed gases...Ch. 11.4 - Tumor growth For Problems 23 and 24, suppose that...Ch. 11.4 - Tumor growth For Problems 23 and 24, suppose that...Ch. 11.4 - 25. Allomelric relationships—fish For many species...Ch. 11.4 - 26. Blood flow The resistance R of a blood vessel...Ch. 11.4 - 27. Allometric relationships—crabs For fiddler...Ch. 11.4 - 28. Body weight and surface area For human beings,...Ch. 11.4 - 29. Cell growth A bacterial cell has a spherical...Ch. 11.4 - 30. Water purification Assume that water is being...Ch. 11.4 - 31. Volume and radius Suppose that air is being...Ch. 11.4 - 32. Boat docking Suppose that a boat is being...Ch. 11.4 - 33. Ladder safety A 30-ft ladder is leaning...Ch. 11.4 - 34. Flight A kite is 30 ft high and is moving...Ch. 11.4 - 35. Flight A plane is flying at a constant...Ch. 11.4 - 36. Distance Two boats leave the same port at the...Ch. 11.4 - 37. Distance Two cars are approaching an...Ch. 11.4 - 38. Water depth Water is flowing into a barrel in...Ch. 11.4 - 39. Water depth Suppose that water is being pumped...Ch. 11.5 - 1. Write the formula for point elasticity, . Ch. 11.5 - 2. (a) If , the demand is called _______. (b) If...Ch. 11.5 - 3. Find the elasticity of demand tor when p = 10...Ch. 11.5 - 4. For problems involving taxation in a...Ch. 11.5 - In Problems 1 -8, p is in dollars and q is the...Ch. 11.5 - In Problems 1 -8, p is in dollars and q is the...Ch. 11.5 - In Problems 1 -8, p is in dollars and q is the...Ch. 11.5 - In Problems 1 -8, p is in dollars and q is the...Ch. 11.5 - In Problems 1 -8, p is in dollars and q is the...Ch. 11.5 - In Problems 1 -8, p is in dollars and q is the...Ch. 11.5 - In Problems 1 -8, p is in dollars and q is the...Ch. 11.5 - In Problems 1 -8, p is in dollars and q is the...Ch. 11.5 - 9. Suppose the demand function for a product is...Ch. 11.5 - 10. Suppose the weekly demand function for a...Ch. 11.5 - In Problems 11 and 12, the demand functions for...Ch. 11.5 - In Problems 11 and 12, the demand functions for...Ch. 11.5 - In Problems 15-24, p is the price per unit in...Ch. 11.5 - In Problems 15-24, p is the price per unit in...Ch. 11.5 - In Problems 15-24, p is the price per unit in...Ch. 11.5 - In Problems 15-24, p is the price per unit in...Ch. 11.5 - In Problems 15-24, p is the price per unit in...Ch. 11.5 - In Problems 15-24, p is the price per unit in...Ch. 11.5 - In Problems 15-24, p is the price per unit in...Ch. 11.5 - In Problems 15-24, p is the price per unit in...Ch. 11.5 - In Problems 15-24, p is the price per unit in...Ch. 11.5 - In Problems 15-24, p is the price per unit in...Ch. 11 - In Problems 1-12, find the derivative of each...Ch. 11 - In Problems 1-12, find the derivative of each...Ch. 11 - In Problems 1-12, find the derivative of each...Ch. 11 - In Problems 1-12, find the derivative of each...Ch. 11 - In Problems 1-12, find the derivative of each...Ch. 11 - In Problems 1-12, find the derivative of each...Ch. 11 - In Problems 1-12, find the derivative of each...Ch. 11 - In Problems 1-12, find the derivative of each...Ch. 11 - In Problems 1-12, find the derivative of each...Ch. 11 - In Problems 1-12, find the derivative of each...Ch. 11 - In Problems 1-12, find the derivative of each...Ch. 11 - In Problems 1-12, find the derivative of each...Ch. 11 - 13. Write the equation of the line tangent to Ch. 11 - 14. At write the equation of the line tangent to...Ch. 11 - In Problems 15-20, find the indicated...Ch. 11 - In Problems 15-20, find the indicated...Ch. 11 - In Problems 15-20, find the indicated...Ch. 11 - In Problems 15-20, find the indicated...Ch. 11 - In Problems 15-20, find the indicated...Ch. 11 - In Problems 15-20, find the indicated...Ch. 11 - 21. Find the slope of the tangent to the curve Ch. 11 - 22. Find the points where tangents to the graph of...Ch. 11 - 23. Suppose where x and y are differentiable...Ch. 11 - 24. A right triangle with legs of lengths x and y...Ch. 11 - 25. Demographics Using U.S. Census Bureau data for...Ch. 11 - 26. Life expectancy at age 65 Using Social...Ch. 11 - 27. Compound interest If $1000 is invested for n...Ch. 11 - 28. Disposable income Disposable income is the...Ch. 11 - 29. Radioactive decay A breeder reactor converts...Ch. 11 - 30. Marginal cost The average cost of producing x...Ch. 11 - 31. Inflation The impact of inflation on a $60,000...Ch. 11 - 32. Evaporation A spherical droplet of water...Ch. 11 - 33. Worker safety A sign is being lowered over the...Ch. 11 - 34. Environment Suppose that in a study of water...Ch. 11 - 35. Elasticity A demand function is given...Ch. 11 - 36. Elasticity Suppose the demand for a product is...Ch. 11 - 37. Elasticity Suppose the weekly demand function...Ch. 11 - 38. Revenue A product has the demand...Ch. 11 - 39. Taxes Can increasing the tax per unit sold...Ch. 11 - 40. Taxes Suppose the demand and supply functions...Ch. 11 - 41. Taxes Suppose the supply and demand functions...Ch. 11 - In Problems 1-8, find the derivative of each...Ch. 11 - In Problems 1-8, find the derivative of each...Ch. 11 - In Problems 1-8, find the derivative of each...Ch. 11 - In Problems 1-8, find the derivative of each...Ch. 11 - In Problems 1-8, find the derivative of each...Ch. 11 - In Problems 1-8, find the derivative of each...Ch. 11 - In Problems 1-8, find the derivative of each...Ch. 11 - In Problems 1-8, find the derivative of each...Ch. 11 - 9. Find y’ if . Ch. 11 - 10. Let If , find when x = 6 and y = 8. Ch. 11 - 11. Find y’ if . Ch. 11 - 12. Suppose the weekly revenue and weekly cost...Ch. 11 - 13. Suppose the demand for a product is , where p...Ch. 11 - 14. Suppose the demand function for a product is...Ch. 11 - 15. The sales of a product are given by , where S...Ch. 11 - 16. Using U.S. Centers for Medicare and Medicaid...Ch. 11 - 17. Suppose the demand and supply functions for a...Ch. 11 - 19. Prices for goods and services tend to rise...

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