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).
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).
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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Transcribed Image Text: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).
2
3
Then a =
=
and b =
2. Absolute minimum of f(x, y) is
and absolute maximum is 8
X
X
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