Suppose that f(x, y) = x² – xy + y² – lx + ly {(x, y) | 0 < y < æ < 1}. - - 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 = 1 2 and b 2. Absolute minimum of f(x, y) is and absolute maximum is 1

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.3: Maxima And Minima
Problem 31E
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Suppose that f (x, y) = x²
– xy + y? – læ + 1y
%3D
-
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
(а, b). Then
a —
1
2
and b
2. Absolute minimum of f(x, y) is
and absolute maximum is
1
Transcribed Image Text:Suppose that f (x, y) = x² – xy + y? – læ + 1y %3D - 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 (а, b). Then a — 1 2 and b 2. Absolute minimum of f(x, y) is and absolute maximum is 1
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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,