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Exam 8: Functions of Several Variables

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Exam 1: Functions and Change204 Questionsadd course
Exam 2: Rate of Change: the Derivative132 Questionsadd course
Exam 3: Shortcuts to Differentiation178 Questionsadd course
Exam 4: Using the Derivative94 Questionsadd course
Exam 5: Accumulated Change: the Definite Integral93 Questionsadd course
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Exam 9: Mathematical Modeling Using Differential Equations121 Questionsadd course
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The heat index tells you how hot it feels as a result of the combination of temperature and humidity. The figure below gives a contour diagram for the heat index as a function of temperature and humidity. If the humidity is 30%, what temperature feels like 90 The heat index tells you how hot it feels as a result of the combination of temperature and humidity. The figure below gives a contour diagram for the heat index as a function of temperature and humidity. If the humidity is 30%, what temperature feels like 90 ? ? The heat index tells you how hot it feels as a result of the combination of temperature and humidity. The figure below gives a contour diagram for the heat index as a function of temperature and humidity. If the humidity is 30%, what temperature feels like 90 ?

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Question 61

For For , calculate f<sub>xx</sub> (x,y). , calculate fxx (x,y).

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Question 62

Lift ticket sales, S, at a ski resort are a function of the price, p, of a ticket and the current number, n, of inches of snowpack on the mountain. Thus, Lift ticket sales, S, at a ski resort are a function of the price, p, of a ticket and the current number, n, of inches of snowpack on the mountain. Thus, . Do you expect f to be an increasing or a decreasing function of n? . Do you expect f to be an increasing or a decreasing function of n?

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Question 63

If If , does f<sub>yy</sub> <sub> </sub> = ? , does fyy If , does f<sub>yy</sub> <sub> </sub> = ? = If , does f<sub>yy</sub> <sub> </sub> = ? ?

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Question 64

A mop company can produce A mop company can produce mops using x units of capital and y units of labor, with production costs dollars. With a budget of $550,000, the maximum production is 65,000 mops, using $400,000 in capital and $150,000 in labor. The Lagrange multiplier is . Which of the following is true? mops using x units of capital and y units of labor, with production costs A mop company can produce mops using x units of capital and y units of labor, with production costs dollars. With a budget of $550,000, the maximum production is 65,000 mops, using $400,000 in capital and $150,000 in labor. The Lagrange multiplier is . Which of the following is true? dollars. With a budget of $550,000, the maximum production is 65,000 mops, using $400,000 in capital and $150,000 in labor. The Lagrange multiplier is A mop company can produce mops using x units of capital and y units of labor, with production costs dollars. With a budget of $550,000, the maximum production is 65,000 mops, using $400,000 in capital and $150,000 in labor. The Lagrange multiplier is . Which of the following is true? . Which of the following is true?

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Question 65

The following is a contour diagram for The following is a contour diagram for . Is f<sub>x</sub> <sub> </sub> positive or negative? . Is fx The following is a contour diagram for . Is f<sub>x</sub> <sub> </sub> positive or negative? positive or negative? The following is a contour diagram for . Is f<sub>x</sub> <sub> </sub> positive or negative?

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Question 66

The heat index tells you how hot it feels as a result of the combination of temperature and humidity. The figure below gives a contour diagram for the heat index as a function of temperature and humidity. Fix the humidity level at 50%. As the temperature rises, does the heat index rise more rapidly at milder temperatures (70 The heat index tells you how hot it feels as a result of the combination of temperature and humidity. The figure below gives a contour diagram for the heat index as a function of temperature and humidity. Fix the humidity level at 50%. As the temperature rises, does the heat index rise more rapidly at milder temperatures (70 to 90 ) or at very hot temperatures (90 to 110 )? to 90 The heat index tells you how hot it feels as a result of the combination of temperature and humidity. The figure below gives a contour diagram for the heat index as a function of temperature and humidity. Fix the humidity level at 50%. As the temperature rises, does the heat index rise more rapidly at milder temperatures (70 to 90 ) or at very hot temperatures (90 to 110 )? ) or at very hot temperatures (90 The heat index tells you how hot it feels as a result of the combination of temperature and humidity. The figure below gives a contour diagram for the heat index as a function of temperature and humidity. Fix the humidity level at 50%. As the temperature rises, does the heat index rise more rapidly at milder temperatures (70 to 90 ) or at very hot temperatures (90 to 110 )? to 110 The heat index tells you how hot it feels as a result of the combination of temperature and humidity. The figure below gives a contour diagram for the heat index as a function of temperature and humidity. Fix the humidity level at 50%. As the temperature rises, does the heat index rise more rapidly at milder temperatures (70 to 90 ) or at very hot temperatures (90 to 110 )? )? The heat index tells you how hot it feels as a result of the combination of temperature and humidity. The figure below gives a contour diagram for the heat index as a function of temperature and humidity. Fix the humidity level at 50%. As the temperature rises, does the heat index rise more rapidly at milder temperatures (70 to 90 ) or at very hot temperatures (90 to 110 )?

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Question 67

If If , find f<sub>x</sub> <sub> </sub> . , find fx If , find f<sub>x</sub> <sub> </sub> . .

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Question 68

The demand, D, for gasoline at Station A is a function of the price, a, of gas at Station A and the price, b, of gas at Station B across the street. Thus, The demand, D, for gasoline at Station A is a function of the price, a, of gas at Station A and the price, b, of gas at Station B across the street. Thus, . Do you expect b to be positive or negative? . Do you expect The demand, D, for gasoline at Station A is a function of the price, a, of gas at Station A and the price, b, of gas at Station B across the street. Thus, . Do you expect b to be positive or negative? b to be positive or negative?

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Question 69

The function The function has a local maximum value of _____ when x = _____ and y = _____. has a local maximum value of _____ when x = _____ and y = _____.

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Question 70

The following figure is a contour diagram for the demand for pork as a function of the price of pork and the price of beef. Which axis corresponds to the price of beef? The following figure is a contour diagram for the demand for pork as a function of the price of pork and the price of beef. Which axis corresponds to the price of beef?

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Question 71

The amount in dollars, A, spent weekly by a household on food is a function of the household's weekly income in dollars, I, and the number of people in the household, n. Thus, The amount in dollars, A, spent weekly by a household on food is a function of the household's weekly income in dollars, I, and the number of people in the household, n. Thus, . If A<sub>I</sub> (1000, 4) = a > 0, then which of the following is true? . If AI (1000, 4) = a > 0, then which of the following is true?

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Question 72

Let Let Determine all local critical points. Are the local extrema also global extrema? Determine all local critical points. Are the local extrema also global extrema?

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Question 73

Your monthly payment, C(s, t), on a car loan depends on the amount, s, of the loan (in thousands of dollars), and the time, t, required to pay it back (in months). What is the meaning of C(6, 24) = 200?

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Question 74

A company sells two styles of jeans in quantities A company sells two styles of jeans in quantities and at prices and respectively, with and in dollars. The quantities demanded depend on both and according to the formulas and . Write a formula for total sales revenue as a function of and , and use it to determine what prices the company should charge to maximize sales revenue. They should charge $_____ for style and $_____ for style . and A company sells two styles of jeans in quantities and at prices and respectively, with and in dollars. The quantities demanded depend on both and according to the formulas and . Write a formula for total sales revenue as a function of and , and use it to determine what prices the company should charge to maximize sales revenue. They should charge $_____ for style and $_____ for style . at prices A company sells two styles of jeans in quantities and at prices and respectively, with and in dollars. The quantities demanded depend on both and according to the formulas and . Write a formula for total sales revenue as a function of and , and use it to determine what prices the company should charge to maximize sales revenue. They should charge $_____ for style and $_____ for style . and A company sells two styles of jeans in quantities and at prices and respectively, with and in dollars. The quantities demanded depend on both and according to the formulas and . Write a formula for total sales revenue as a function of and , and use it to determine what prices the company should charge to maximize sales revenue. They should charge $_____ for style and $_____ for style . respectively, with A company sells two styles of jeans in quantities and at prices and respectively, with and in dollars. The quantities demanded depend on both and according to the formulas and . Write a formula for total sales revenue as a function of and , and use it to determine what prices the company should charge to maximize sales revenue. They should charge $_____ for style and $_____ for style . and A company sells two styles of jeans in quantities and at prices and respectively, with and in dollars. The quantities demanded depend on both and according to the formulas and . Write a formula for total sales revenue as a function of and , and use it to determine what prices the company should charge to maximize sales revenue. They should charge $_____ for style and $_____ for style . in dollars. The quantities demanded depend on both A company sells two styles of jeans in quantities and at prices and respectively, with and in dollars. The quantities demanded depend on both and according to the formulas and . Write a formula for total sales revenue as a function of and , and use it to determine what prices the company should charge to maximize sales revenue. They should charge $_____ for style and $_____ for style . and A company sells two styles of jeans in quantities and at prices and respectively, with and in dollars. The quantities demanded depend on both and according to the formulas and . Write a formula for total sales revenue as a function of and , and use it to determine what prices the company should charge to maximize sales revenue. They should charge $_____ for style and $_____ for style . according to the formulas A company sells two styles of jeans in quantities and at prices and respectively, with and in dollars. The quantities demanded depend on both and according to the formulas and . Write a formula for total sales revenue as a function of and , and use it to determine what prices the company should charge to maximize sales revenue. They should charge $_____ for style and $_____ for style . and A company sells two styles of jeans in quantities and at prices and respectively, with and in dollars. The quantities demanded depend on both and according to the formulas and . Write a formula for total sales revenue as a function of and , and use it to determine what prices the company should charge to maximize sales revenue. They should charge $_____ for style and $_____ for style . . Write a formula for total sales revenue as a function of A company sells two styles of jeans in quantities and at prices and respectively, with and in dollars. The quantities demanded depend on both and according to the formulas and . Write a formula for total sales revenue as a function of and , and use it to determine what prices the company should charge to maximize sales revenue. They should charge $_____ for style and $_____ for style . and A company sells two styles of jeans in quantities and at prices and respectively, with and in dollars. The quantities demanded depend on both and according to the formulas and . Write a formula for total sales revenue as a function of and , and use it to determine what prices the company should charge to maximize sales revenue. They should charge $_____ for style and $_____ for style . , and use it to determine what prices the company should charge to maximize sales revenue. They should charge $_____ for style A company sells two styles of jeans in quantities and at prices and respectively, with and in dollars. The quantities demanded depend on both and according to the formulas and . Write a formula for total sales revenue as a function of and , and use it to determine what prices the company should charge to maximize sales revenue. They should charge $_____ for style and $_____ for style . and $_____ for style A company sells two styles of jeans in quantities and at prices and respectively, with and in dollars. The quantities demanded depend on both and according to the formulas and . Write a formula for total sales revenue as a function of and , and use it to determine what prices the company should charge to maximize sales revenue. They should charge $_____ for style and $_____ for style . .

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Question 75

Find all the critical points of Find all the critical points of and classify each as maximum, minimum, or neither. Select all possible choices. and classify each as maximum, minimum, or neither. Select all possible choices.

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Question 76

A contour diagram of A contour diagram of is given in the following figure. Which one of the following statements is true? is given in the following figure. Which one of the following statements is true? A contour diagram of is given in the following figure. Which one of the following statements is true?

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Question 77

You are in a nicely heated cabin in the winter. Deciding that it's too warm, you open a small window. Let T be the temperature in the room, t minutes after the window was opened, x feet from the window. Is T an increasing or decreasing function of x?

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Question 78

A contour diagram of A contour diagram of is given in the following figure. Is there a global minimum near the point (5,3)? is given in the following figure. Is there a global minimum near the point (5,3)? A contour diagram of is given in the following figure. Is there a global minimum near the point (5,3)?

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Question 79

The point (0, 2) is a critical point of The point (0, 2) is a critical point of Classify it either as a local minimum, local maximum, or neither. Classify it either as a local minimum, local maximum, or neither.

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Question 80
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