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Problem 2. A manufacturing company developed a mathematical model to predict its expenses as a function of two variables: f (x, y) = 4x° + y° -12x – 3y + 25 . Both variables, x and y are quantitative, and can only accept continuous values between –1 and 1, including those points*. *Note that this is equivalent to saying that the domain of this function is -1

Problem 2. A manufacturing company developed a mathematical model to predict its expenses as a function of two variables: f (x, y) = 4x° + y° -12x – 3y + 25 . Both variables, x and y are quantitative, and can only accept continuous values between –1 and 1, including those points*. *Note that this is equivalent to saying that the domain of this function is -1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 2. A manufacturing company developed a mathematical model to predict its expenses as a function of two variables: f (x, y) = 4x° +y° -12x - 3y + 25 . Both variables, x and y are quantitative, and can only accept continuous values between –1 and 1, including those points*. *Note that this is equivalent to saying that the domain of this function is -1 <x S1 and –1<ys1. a. Obtain the first partial derivatives of the function. b. What does it mean that the first partial derivatives are both zero at the same time? c. Find all second order derivatives. How many of them distinct can be computed? Explain. d. Employ a test to determine values of x & y such that expenses are maximum and minimum. e. Which is the range of this company's expenses? Explain how you can be certain
Transcribed Image Text:Problem 2. A manufacturing company developed a mathematical model to predict its expenses as a function of two variables: f (x, y) = 4x° +y° -12x - 3y + 25 . Both variables, x and y are quantitative, and can only accept continuous values between –1 and 1, including those points*. *Note that this is equivalent to saying that the domain of this function is -1 <x S1 and –1<ys1. a. Obtain the first partial derivatives of the function. b. What does it mean that the first partial derivatives are both zero at the same time? c. Find all second order derivatives. How many of them distinct can be computed? Explain. d. Employ a test to determine values of x & y such that expenses are maximum and minimum. e. Which is the range of this company's expenses? Explain how you can be certain
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