Explore all topics
Start Free Trial
Need Help? Contact us
back arrowfull exam logo
search
ai logoChat with AI
Servicesarrow
Discoverarrow

Topics

Explore all topics
Discover more topics

Exam 8: Functions of Several Variables

arrow
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
Exam 6: Antiderivatives and Applications122 Questionsadd course
Exam 7: Probability68 Questionsadd course
Exam 8: Functions of Several Variables134 Questionsadd course
Exam 9: Mathematical Modeling Using Differential Equations121 Questionsadd course
Exam 10: Geometric Series65 Questionsadd course
Select questions type
  • Essay
  • Multiple Choice
  • Short Answer
  • True False
  • Matching
  • Select Tags
search iconSearch Question
flashcardsStudy Flashcards
Select questions type
  • Essay
  • Multiple Choice
  • Short Answer
  • True False
  • Matching
  • Select Tags

Suppose that Suppose that Find and classify (as local maxima, minima, or neither) all critical points of f. Find and classify (as local maxima, minima, or neither) all critical points of f.

(Short Answer)
4.9/5
(32)
Question 21

The fuel cost, C, for a 3000 mile trip depends on the price, p, per gallon of gasoline and fuel economy in miles per gallon, m, of the car according to the formula The fuel cost, C, for a 3000 mile trip depends on the price, p, per gallon of gasoline and fuel economy in miles per gallon, m, of the car according to the formula . On the same set of axes, sketch a graph of C as a function of m with fixed gas prices of $2.00, $2.25, $2.50, and $2.75. What do you observe as gas prices increase? . On the same set of axes, sketch a graph of C as a function of m with fixed gas prices of $2.00, $2.25, $2.50, and $2.75. What do you observe as gas prices increase?

(Multiple Choice)
4.8/5
(35)
Question 22

The function The function has a local minimum at (1, 2.5). Which of the following is a sketch of the level curves of f near this point? has a local minimum at (1, 2.5). Which of the following is a sketch of the level curves of f near this point?

(Multiple Choice)
4.9/5
(33)
Question 23

The number, N, of children that can be enrolled in a private school is a function of the number of certified teachers, T, and the number of aides, A, available, according to the formula The number, N, of children that can be enrolled in a private school is a function of the number of certified teachers, T, and the number of aides, A, available, according to the formula . Teachers average an annual salary of $38,000 and aides average an annual salary of $20,000. The annual budget for salaries is B = $800,000. If we want to maximize enrollment, which of the following is true? . Teachers average an annual salary of $38,000 and aides average an annual salary of $20,000. The annual budget for salaries is B = $800,000. If we want to maximize enrollment, which of the following is true?

(Multiple Choice)
4.9/5
(33)
Question 24

The quantity, Q, of a good produced depends on the number of workers, W, and the amount of capital invested, K, according to the Cobb-Douglas function The quantity, Q, of a good produced depends on the number of workers, W, and the amount of capital invested, K, according to the Cobb-Douglas function . In addition, we know that labor costs are $19 per employee, capital costs are $8 per unit, and the budget is $2500. The maximum production level is about _____ units, where W = _____ and K = _____. Round to the nearest whole number. . In addition, we know that labor costs are $19 per employee, capital costs are $8 per unit, and the budget is $2500. The maximum production level is about _____ units, where W = _____ and K = _____. Round to the nearest whole number.

(Short Answer)
4.9/5
(38)
Question 25

The critical point of The critical point of occurs at x = _____, y = _____, and is a local ________ (maximum / minimum / neither). occurs at x = _____, y = _____, and is a local ________ (maximum / minimum / neither).

(Short Answer)
4.8/5
(28)
Question 26

The quantity, Q, of a good produced depends on the quantities The quantity, Q, of a good produced depends on the quantities and of the two main materials used: . Material costs $55 per unit, and material costs $70 per unit. We want to minimize the cost of producing 100 units of the good. Using Lagrange multipliers, we see that the minimum cost of ________ occurs when = _____ and = _____. and The quantity, Q, of a good produced depends on the quantities and of the two main materials used: . Material costs $55 per unit, and material costs $70 per unit. We want to minimize the cost of producing 100 units of the good. Using Lagrange multipliers, we see that the minimum cost of ________ occurs when = _____ and = _____. of the two main materials used: The quantity, Q, of a good produced depends on the quantities and of the two main materials used: . Material costs $55 per unit, and material costs $70 per unit. We want to minimize the cost of producing 100 units of the good. Using Lagrange multipliers, we see that the minimum cost of ________ occurs when = _____ and = _____. . Material The quantity, Q, of a good produced depends on the quantities and of the two main materials used: . Material costs $55 per unit, and material costs $70 per unit. We want to minimize the cost of producing 100 units of the good. Using Lagrange multipliers, we see that the minimum cost of ________ occurs when = _____ and = _____. costs $55 per unit, and material The quantity, Q, of a good produced depends on the quantities and of the two main materials used: . Material costs $55 per unit, and material costs $70 per unit. We want to minimize the cost of producing 100 units of the good. Using Lagrange multipliers, we see that the minimum cost of ________ occurs when = _____ and = _____. costs $70 per unit. We want to minimize the cost of producing 100 units of the good. Using Lagrange multipliers, we see that the minimum cost of ________ occurs when The quantity, Q, of a good produced depends on the quantities and of the two main materials used: . Material costs $55 per unit, and material costs $70 per unit. We want to minimize the cost of producing 100 units of the good. Using Lagrange multipliers, we see that the minimum cost of ________ occurs when = _____ and = _____. = _____ and The quantity, Q, of a good produced depends on the quantities and of the two main materials used: . Material costs $55 per unit, and material costs $70 per unit. We want to minimize the cost of producing 100 units of the good. Using Lagrange multipliers, we see that the minimum cost of ________ occurs when = _____ and = _____. = _____.

(Short Answer)
4.7/5
(33)
Question 27

Two products are manufactured in quantities Two products are manufactured in quantities and and sold at prices $8 and $12 respectively. The cost of producing them is given by . Find the maximum profit that can be made. and Two products are manufactured in quantities and and sold at prices $8 and $12 respectively. The cost of producing them is given by . Find the maximum profit that can be made. and sold at prices $8 and $12 respectively. The cost of producing them is given by Two products are manufactured in quantities and and sold at prices $8 and $12 respectively. The cost of producing them is given by . Find the maximum profit that can be made. . Find the maximum profit that can be made.

(Short Answer)
4.9/5
(48)
Question 28

The production function for a company is The production function for a company is , where P is the amount produced given x units of labor and y units of equipment. Each unit of labor costs $900 and each unit of equipment costs $400. Assuming the goal of the company is to maximize production given a fixed budget of $40,000, what is the meaning of the Lagrange multiplier ? , where P is the amount produced given x units of labor and y units of equipment. Each unit of labor costs $900 and each unit of equipment costs $400. Assuming the goal of the company is to maximize production given a fixed budget of $40,000, what is the meaning of the Lagrange multiplier The production function for a company is , where P is the amount produced given x units of labor and y units of equipment. Each unit of labor costs $900 and each unit of equipment costs $400. Assuming the goal of the company is to maximize production given a fixed budget of $40,000, what is the meaning of the Lagrange multiplier ? ?

(Multiple Choice)
4.7/5
(26)
Question 29

Let Let where k \neq 0. Find the critical points of f. where k ≠\neq 0. Find the critical points of f.

(Short Answer)
4.9/5
(38)
Question 30

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). Is C an increasing or decreasing function of t?

(Multiple Choice)
4.9/5
(37)
Question 31

The quantity, Q, of a good produced depends on the quantities The quantity, Q, of a good produced depends on the quantities and of the two main materials used: . Material costs $100 per unit, and material costs $25 per unit. We want to minimize the cost of producing 100 units of the good. What is the objective function? and The quantity, Q, of a good produced depends on the quantities and of the two main materials used: . Material costs $100 per unit, and material costs $25 per unit. We want to minimize the cost of producing 100 units of the good. What is the objective function? of the two main materials used: The quantity, Q, of a good produced depends on the quantities and of the two main materials used: . Material costs $100 per unit, and material costs $25 per unit. We want to minimize the cost of producing 100 units of the good. What is the objective function? . Material The quantity, Q, of a good produced depends on the quantities and of the two main materials used: . Material costs $100 per unit, and material costs $25 per unit. We want to minimize the cost of producing 100 units of the good. What is the objective function? costs $100 per unit, and material The quantity, Q, of a good produced depends on the quantities and of the two main materials used: . Material costs $100 per unit, and material costs $25 per unit. We want to minimize the cost of producing 100 units of the good. What is the objective function? costs $25 per unit. We want to minimize the cost of producing 100 units of the good. What is the objective function?

(Multiple Choice)
4.7/5
(37)
Question 32

A table of values for A table of values for is given below. Estimate f<sub>y</sub> (8,10). Use the next higher point to make your estimate. is given below. Estimate fy (8,10). Use the next higher point to make your estimate. A table of values for is given below. Estimate f<sub>y</sub> (8,10). Use the next higher point to make your estimate.

(Short Answer)
4.8/5
(47)
Question 33

Find the critical points of Find the critical points of and classify each as maximum, minimum or neither. and classify each as maximum, minimum or neither.

(Essay)
4.9/5
(32)
Question 34

The monthly mortgage payment in dollars, P, for a house is a function of three variables P = f(A, r, N), where A is the amount borrowed in dollars, r is the interest rate, and N is the number of years before the mortgage is paid off. It is given that: The monthly mortgage payment in dollars, P, for a house is a function of three variables P = f(A, r, N), where A is the amount borrowed in dollars, r is the interest rate, and N is the number of years before the mortgage is paid off. It is given that: Estimate the value of Estimate the value of The monthly mortgage payment in dollars, P, for a house is a function of three variables P = f(A, r, N), where A is the amount borrowed in dollars, r is the interest rate, and N is the number of years before the mortgage is paid off. It is given that: Estimate the value of

(Short Answer)
4.9/5
(43)
Question 35

The following figure shows contours of The following figure shows contours of and the constraint . What is the value of x that maximizes f subject to this constraint? and the constraint The following figure shows contours of and the constraint . What is the value of x that maximizes f subject to this constraint? . What is the value of x that maximizes f subject to this constraint? The following figure shows contours of and the constraint . What is the value of x that maximizes f subject to this constraint?

(Short Answer)
5.0/5
(40)
Question 36

Suppose the Cobb-Douglas production function for a company is given by Suppose the Cobb-Douglas production function for a company is given by , where P is production in tons, L is the number of workers, and K is the capital investment, in thousands of dollars. How many tons are produced if the company has an initial investment of 20 thousand dollars and the company employs 16 workers? Round to the nearest ton. , where P is production in tons, L is the number of workers, and K is the capital investment, in thousands of dollars. How many tons are produced if the company has an initial investment of 20 thousand dollars and the company employs 16 workers? Round to the nearest ton.

(Short Answer)
4.9/5
(33)
Question 37

An airline's revenue, An airline's revenue, , is a function of the number of full price tickets, x, and the number of discount tickets, y, sold. When 300 full price and 600 discount tickets are sold, R = $225,000. Use partial derivatives and to estimate revenue when x = 304 and y = 603. , is a function of the number of full price tickets, x, and the number of discount tickets, y, sold. When 300 full price and 600 discount tickets are sold, R = $225,000. Use partial derivatives An airline's revenue, , is a function of the number of full price tickets, x, and the number of discount tickets, y, sold. When 300 full price and 600 discount tickets are sold, R = $225,000. Use partial derivatives and to estimate revenue when x = 304 and y = 603. and An airline's revenue, , is a function of the number of full price tickets, x, and the number of discount tickets, y, sold. When 300 full price and 600 discount tickets are sold, R = $225,000. Use partial derivatives and to estimate revenue when x = 304 and y = 603. to estimate revenue when x = 304 and y = 603.

(Short Answer)
4.8/5
(30)
Question 38

If If , find r<sup>2.</sup> , find If , find r<sup>2.</sup> r2.

(Multiple Choice)
4.8/5
(28)
Question 39

The following figure shows contours for the function The following figure shows contours for the function . Is z an increasing or decreasing function of x? . Is z an increasing or decreasing function of x? The following figure shows contours for the function . Is z an increasing or decreasing function of x?

(Short Answer)
4.9/5
(33)
Question 40
Showing 21 - 40 of 134
close modal

Filters

  • Essay(0)
  • Multiple Choice(0)
  • Short Answer(0)
  • True False(0)
  • Matching(0)