Minimize f(x,y) = x² + xy + y² subject to y = -6 without using the method of Lagrange multipliers; instead, solve the constraint for x or y and substitute into f(x,y). Use the constraint to rewrite f(x,y) = x² + xy + y² as a function of one variable, g(x). g(x) = The minimum value of f(x,y) = x² + xy + y² subject to y = -6 occurs at the point. (Type an ordered pair.) The minimum value of f(x,y) = x² + xy + y² subject to y = -6 is (Simplify your answer.)
Minimize f(x,y) = x² + xy + y² subject to y = -6 without using the method of Lagrange multipliers; instead, solve the constraint for x or y and substitute into f(x,y). Use the constraint to rewrite f(x,y) = x² + xy + y² as a function of one variable, g(x). g(x) = The minimum value of f(x,y) = x² + xy + y² subject to y = -6 occurs at the point. (Type an ordered pair.) The minimum value of f(x,y) = x² + xy + y² subject to y = -6 is (Simplify your answer.)
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CR: Review Problem Set
Problem 37CR
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![Minimize f(x,y) = x² + xy + y² subject to y = -6 without using the method of Lagrange multipliers; instead, solve the constraint for x or y and substitute into f(x,y).
Use the constraint to rewrite f(x,y) = x² + xy + y² as a function of one variable, g(x).
g(x)
=
The minimum value of f(x,y) = x² + xy + y² subject to y = -6 occurs at the point
(Type an ordered pair.)
The minimum value of f(x,y) = x² + xy + y² subject to y = -6 is
(Simplify your answer.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b1cab43-2155-41da-a401-15f3493c67ce%2Faa0d42c2-77e4-40d4-b545-26a498659698%2F0c2w0g_processed.png&w=3840&q=75)
Transcribed Image Text:Minimize f(x,y) = x² + xy + y² subject to y = -6 without using the method of Lagrange multipliers; instead, solve the constraint for x or y and substitute into f(x,y).
Use the constraint to rewrite f(x,y) = x² + xy + y² as a function of one variable, g(x).
g(x)
=
The minimum value of f(x,y) = x² + xy + y² subject to y = -6 occurs at the point
(Type an ordered pair.)
The minimum value of f(x,y) = x² + xy + y² subject to y = -6 is
(Simplify your answer.)
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