Answered: Find the maximum and minimum values of…

Find the maximum and minimum values of the function f(x, y) = xy on the closed and bounded region defined as {(x, y) | x^2 + y^2 ≤ 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 19E

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Question

Find the maximum and minimum values of the function f(x, y) = xy on the closed and bounded region defined as {(x, y) | x^2 + y^2 ≤ 1}.

[Hint: You need to analyze the function first on the open region {(x, y) | x^2 + y^2 < 1} and then on the boundary {(x, y) | x^2 + y^2 = 1}.]

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