Find the maximum and minimum values of f(x, y) = x² - 2y - y² subject to x² + y² ≤ 4. (a) Use methods from section 14.7 to find the critical points of f(x, y) in the region x² + y² < 4. (b) Use Lagrange multipliers to find critical points of f(x, y) on the boundary x² + y² = 4. (c) Determine the absolute maximum and minimum.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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8. Find the maximum and minimum values of f(x, y) = x² - 2y - y² subject to x² + y² ≤ 4.
(a) Use methods from section 14.7 to find the critical points of f(x, y) in the region x² + y² < 4.
(b) Use Lagrange multipliers to find critical points of f(x, y) on the boundary x² + y² = 4.
(c) Determine the absolute maximum and minimum.
Transcribed Image Text:8. Find the maximum and minimum values of f(x, y) = x² - 2y - y² subject to x² + y² ≤ 4. (a) Use methods from section 14.7 to find the critical points of f(x, y) in the region x² + y² < 4. (b) Use Lagrange multipliers to find critical points of f(x, y) on the boundary x² + y² = 4. (c) Determine the absolute maximum and minimum.
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