Suppose that f(x, y) = x² – xy+ y² – x + y with D = {(x, y) |0 < y< x < 1}. 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 absolute nmaximum is
Suppose that f(x, y) = x² – xy+ y² – x + y with D = {(x, y) |0 < y< x < 1}. 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 absolute nmaximum is
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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![Suppose that \( f(x, y) = x^2 - xy + y^2 - x + y \) with \( D = \{(x, y) \,|\, 0 \leq y \leq x \leq 1\} \).
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 absolute maximum is
\[
\_\_\_\_\_\_
\].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3641f861-3f15-4a36-adeb-305d1cfb07ba%2F9b302d44-5e79-42c3-9ebf-58ff6e56831a%2Fw290fto_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that \( f(x, y) = x^2 - xy + y^2 - x + y \) with \( D = \{(x, y) \,|\, 0 \leq y \leq x \leq 1\} \).
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 absolute maximum is
\[
\_\_\_\_\_\_
\].
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