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12th Edition

Ronald J. Harshbarger + 1 other

Publisher: Cengage Learning

ISBN: 9781337625340

Chapter 14.4, Problem 4E

Textbook Problem

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In Problems 1-16, find each function’s relative maxima, relative minima, and saddle points, if they exist.

To determine

**To calculate:** The relative maxima, relative minima, and saddle points of

**Given Information:**

The provided function is

**Formula used:**

Differentiate *x* by holding *y* constant as:

Differentiate *y* by holding *x* constant as:

The every differentiable function

The following procedure are used to calculate relative maximum and saddle point of given function

Step-1: Calculate first derivative of function *x* and *y*.

Step-2 Calculate second derivative of function *x* and *y*.

Step-3: Equate first derivative of function *x* to zero.

Step-4: Equate first derivative of function *y* to zero.

Step-5: Calculate critical point of function

Step-6: Now test function

Critical point | Conclusion | ||

The function |
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The function |
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The function |
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The test gives no information. |

The simple power rule of derivative:

The constant rule of derivative:

The derivative of constant coefficient:

**Calculation:**

Consider the function,

Differentiate *x* by holding *y* constant,

Equate the first derivative of function *x* to zero

Mathematical Applications for the Management, Life, and Social Sciences

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Ch. 14.1 - CHECKPOINT
1. Find the domain of the function
Ch. 14.1 - CHECKPOINT
2. (a) If .
(b) If .
Ch. 14.1 - Give the domain of each function in Problems...Ch. 14.1 - Give the domain of each function in Problems...Ch. 14.1 - Give the domain of each function in Problems...Ch. 14.1 - Give the domain of each function in Problems...Ch. 14.1 - Give the domain of each function in Problems...Ch. 14.1 - Give the domain of each function in Problems...Ch. 14.1 - Give the domain of each function in Problems...Ch. 14.1 - Give the domain of each function in Problems...

Ch. 14.1 - In Problems 9-14, evaluate the functions at the...Ch. 14.1 - In Problems 9-14, evaluate the functions at the...Ch. 14.1 - In Problems 9-14, evaluate the functions at the...Ch. 14.1 - In Problems 9-14, evaluate the functions at the...Ch. 14.1 - In Problems 9-14, evaluate the functions at the...Ch. 14.1 - In Problems 9-14, evaluate the functions at the...Ch. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - 23. Investment The future value S of an investment...Ch. 14.1 - 24. Amortization If $100,000 is borrowed to...Ch. 14.1 - 25. Curve speeds One method traffic planners use...Ch. 14.1 - 26. Wilsons lot size formula In economics, the...Ch. 14.1 - Temperature-humidity models The “feels like”...Ch. 14.1 - Temperature-humidity models The “feels like”...Ch. 14.1 - 29. Mortgage The following tables show that a...Ch. 14.1 - 30. Wind chill Wind and cold temperatures combine...Ch. 14.1 - 31. Utility Suppose that the utility function for...Ch. 14.1 - 32. Utility Suppose that an indifference curve for...Ch. 14.1 - 33. Production Suppose that a company’s production...Ch. 14.1 - 34. Production Suppose that a company’s production...Ch. 14.1 - 35. Production Suppose that the number of units of...Ch. 14.1 - 36. Profit The Kirk Kelly Kandy Company makes two...Ch. 14.1 - 37. Epidemic The cost per day to society of an...Ch. 14.1 - 38. Pesticide An area of land is to be sprayed...Ch. 14.2 - CHECKPOINT
1. If , find the following.
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24. If , find the following.
(a) (b) (c)
Ch. 14.2 -
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(a) (b) (c)
Ch. 14.2 -
26. If , find the following.
(a) (b) (c)
Ch. 14.2 -
27. If , find the following.
(a) (b) (c) (d)...Ch. 14.2 -
28. If , find the following.
(a) (b) (c) (d)...Ch. 14.2 -
29. If , find the following.
(a) (b) (c) (d)...Ch. 14.2 -
30. If , find the following.
(a) (b) (c) (d)...Ch. 14.2 -
31. If , find the following.
(a) (b) (c) (d)...Ch. 14.2 - 32. If , find the following.
(a) (b) (c) (d)
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If the joint cost in dollars for two...Ch. 14.3 - CHECKPOINT
2. If the production function for a...Ch. 14.3 - CHECKPOINT
3. If the demand functions for two...Ch. 14.3 - 1. The cost (in dollars) of manufacturing one item...Ch. 14.3 - 2. The manufacture of 1 unit of a product has a...Ch. 14.3 - 3. The total cost of producing 1 unit of a product...Ch. 14.3 - 4. The total cost of producing an item is
...Ch. 14.3 - 5. The total cost of producing 1 unit of a product...Ch. 14.3 - 6. The total cost of producing 1 unit of a product...Ch. 14.3 - 7. The joint cost (in dollars) for two products is...Ch. 14.3 - 8. The joint cost (in dollars) for products X and...Ch. 14.3 - 9. If the joint cost function for two products is
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tons
is the...Ch. 14.4 - 24. Production Suppose that x units of one input...Ch. 14.4 - 25. Profit Suppose that a manufacturer produces...Ch. 14.4 - 26. Profit Suppose that a firm produces two...Ch. 14.4 - 27. Manufacturing Find the values for each of the...Ch. 14.4 - 28. Manufacturing Find the values for each of the...Ch. 14.4 - 29. Profit A company manufactures two products, A...Ch. 14.4 - 30. Production Let x be the number of work-hours...Ch. 14.4 - The manager of the Sea Islands Chicken Shack is...Ch. 14.4 - The manager of the Sea Islands Chicken Shack is...Ch. 14.4 - 33. Modeling U.S. National consumption The...Ch. 14.4 - 34. Modeling Retirement benefits The following...Ch. 14.4 - 35. Modeling World population The table gives the...Ch. 14.4 - 36. Modeling Student loans The following table...Ch. 14.5 - CHECKPOINT
Find the minimum value of
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Find the minimum value of , subject to...Ch. 14.5 - CHECKPOINT
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Ch. 14.5 - 6. Find the maximum value of the function subject...Ch. 14.5 - 7. Find the maximum value of the function subject...Ch. 14.5 - 8. Find the minimum value of subject to the...Ch. 14.5 - 9. Find the maximum value of subject to .
Ch. 14.5 - 10. Find the maximum value of subject to .
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Ch. 14 - 2. What is the domain of ?
Ch. 14 - 3. If .
Ch. 14 - 4. If .
Ch. 14 - 5. Find .
Ch. 14 - 6. Find .
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Ch. 14 - 13. Find the partial derivative of with respect...Ch. 14 - 14. Find the slope of the tangent in the...Ch. 14 - In Problems 15-18, find the second partials.
Ch. 14 - In Problems 15-18, find the second partials.
Ch. 14 - In Problems 15-18, find the second partials.
Ch. 14 - In Problems 15-18, find the second partials.
Ch. 14 - In Problems 19 and 20, find each function’s...Ch. 14 - In Problems 19 and 20, find each function’s...Ch. 14 - 21. Find the maximum value of subject to the...Ch. 14 - 22. Find the maximum value of subject to the...Ch. 14 - 23. Utility Suppose that the utility function for...Ch. 14 - 24. Savings plans The accumulated value A of a...Ch. 14 - 25. Retirement benefits The monthly benefit B (in...Ch. 14 - 26. Advertising and sales The number of units of...Ch. 14 - 27. Cost The joint cost, in dollars, for two...Ch. 14 - 28. Production Suppose that the production...Ch. 14 - 29. Marginal demand The demand functions for...Ch. 14 - 30. Marginal demand Suppose that the demand...Ch. 14 - 31. Profit The weekly profit (in dollars) from the...Ch. 14 - 32. Cost Suppose a company has two separate plants...Ch. 14 - 33. Utility If the utility function for two...Ch. 14 - 34. Production Suppose a company has the...Ch. 14 - 35. Modeling US. average wage The table gives the...Ch. 14 - 36. Modeling Civilian workforce The following...Ch. 14 - 1. Consider the function .
(a) Find the domain of...Ch. 14 - 2. Find all first and second partial derivatives...Ch. 14 - 3. Let . Find the pairs that are critical points...Ch. 14 - 4. Suppose a company’s monthly production value Q...Ch. 14 - 5. The monthly payment R on a loan is a function...Ch. 14 - 6. Let . Find .
Ch. 14 - 7. Suppose the demand functions for two products...Ch. 14 - 8. Suppose a store sells two brands of disposable...Ch. 14 - 9. Find x and y that maximize the utility function...Ch. 14 - 10. Modeling In the last half of the twentieth...

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