Suppose that f (x, y) = x² − xy +y² − x+y with D = 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 1 Question Help: Video Submit Question Search 11 1000 {(x, y) |0 ≤y≤x≤1}. V ✓o 0 m E 4
Suppose that f (x, y) = x² − xy +y² − x+y with D = 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 1 Question Help: Video Submit Question Search 11 1000 {(x, y) |0 ≤y≤x≤1}. V ✓o 0 m E 4
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 \( D = \{(x, y) \mid 0 \leq y \leq x \leq 1\} \).
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
\[
\frac{1}{4} \quad \checkmark
\]
and the absolute maximum is
\[
1 \quad \checkmark
\]
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Transcribed Image Text:Suppose that \( f(x, y) = x^2 - xy + y^2 - x + y \) with \( D = \{(x, y) \mid 0 \leq y \leq x \leq 1\} \).
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
\[
\frac{1}{4} \quad \checkmark
\]
and the absolute maximum is
\[
1 \quad \checkmark
\]
- Question Help: Video
- Submit Question Button
Diagrams/Graphs:
There are no specific diagrams or graphs provided in the image to describe.
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