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Find the absolute extrema of the function f(x, y) = - 2x² - 2y²+x+y-5 on the domain defined by x² + y² ≤4. Round answers to 3 decimals or more. Absolute Maximum: 5.6 Absolute Minimum: -15.828 Question Help: Video Submit Question X 0 -4.75 OF

Find the absolute extrema of the function f(x, y) = - 2x² - 2y²+x+y-5 on the domain defined by x² + y² ≤4. Round answers to 3 decimals or more. Absolute Maximum: 5.6 Absolute Minimum: -15.828 Question Help: Video Submit Question X 0 -4.75 OF

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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Please explain how -4.75 is the absolute maximum
The task is to find the absolute extrema of the function \( f(x, y) = -2x^2 - 2y^2 + x + y - 5 \) on the domain defined by \( x^2 + y^2 \leq 4 \). **Instructions:** Round answers to 3 decimals or more. **Response Fields:** - Absolute Maximum: The answer given is 5.6, but it is marked incorrect. - Absolute Minimum: The answer given is \(-15.828\), and it is marked correct. **Additional Features:** - A "Question Help" button is available, linked to a video. - A "Submit Question" button for finalizing the answer. This setup is intended for learning purposes, guiding students through the process of finding extrema using calculus while offering resources for assistance.
Transcribed Image Text:The task is to find the absolute extrema of the function \( f(x, y) = -2x^2 - 2y^2 + x + y - 5 \) on the domain defined by \( x^2 + y^2 \leq 4 \). **Instructions:** Round answers to 3 decimals or more. **Response Fields:** - Absolute Maximum: The answer given is 5.6, but it is marked incorrect. - Absolute Minimum: The answer given is \(-15.828\), and it is marked correct. **Additional Features:** - A "Question Help" button is available, linked to a video. - A "Submit Question" button for finalizing the answer. This setup is intended for learning purposes, guiding students through the process of finding extrema using calculus while offering resources for assistance.
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