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Suppose that f(x, y) = x² - xy + y² - 2x + 2y with D = {(x, y) | 0 ≤ y ≤ x ≤ 2}. 1. The critical point of f(x, y) restricted to the boundary of D, not at a corner point, is at (a, b) Then a = and b 2. Absolute minimum of f(x, y) is and the absolute maximum is

Suppose that f(x, y) = x² - xy + y² - 2x + 2y with D = {(x, y) | 0 ≤ y ≤ x ≤ 2}. 1. The critical point of f(x, y) restricted to the boundary of D, not at a corner point, is at (a, b) Then a = and b 2. Absolute minimum of f(x, y) is and the absolute maximum is

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 Statement:** Suppose that \( f(x, y) = x^2 - xy + y^2 - 2x + 2y \) with \( D = \{(x, y) \mid 0 \leq y \leq x \leq 2\} \). 1. The critical point of \( f(x, y) \) restricted to the boundary of \( D \), not at a corner point, is at \((a, b)\). - Then \( a = \) [Fill in the blank] - and \( b = \) [Fill in the blank] 2. Absolute minimum of \( f(x, y) \) is - [Fill in the blank] - and the absolute maximum is - [Fill in the blank].
Transcribed Image Text:**Problem Statement:** Suppose that \( f(x, y) = x^2 - xy + y^2 - 2x + 2y \) with \( D = \{(x, y) \mid 0 \leq y \leq x \leq 2\} \). 1. The critical point of \( f(x, y) \) restricted to the boundary of \( D \), not at a corner point, is at \((a, b)\). - Then \( a = \) [Fill in the blank] - and \( b = \) [Fill in the blank] 2. Absolute minimum of \( f(x, y) \) is - [Fill in the blank] - and the absolute maximum is - [Fill in the blank].
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