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A linear function f (x, y) = ax + by + c has no critical points. Therefore, the global minimum and maximum values of ƒ (x, y) on a closed and bounded domain must occur on the boundary of the domain. Furthermore, it can be easily seen that if the domain is a polygon, then the global minimum and maximum values of f must occur at a vertex of the polygon. Find the global minimum and maximum values of f (x, y) = 4x - 8y-5 on the domain where |x|+ [y] ≤ 8. (Give your answers as a whole numbers.)

A linear function f (x, y) = ax + by + c has no critical points. Therefore, the global minimum and maximum values of ƒ (x, y) on a closed and bounded domain must occur on the boundary of the domain. Furthermore, it can be easily seen that if the domain is a polygon, then the global minimum and maximum values of f must occur at a vertex of the polygon. Find the global minimum and maximum values of f (x, y) = 4x - 8y-5 on the domain where |x|+ [y] ≤ 8. (Give your answers as a whole numbers.)

Calculus For The Life Sciences
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.CR: Chapter 9 Review
Problem 7CR
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A linear function f (x, y) = ax + by + c has no critical points. Therefore, the global minimum and maximum values of f (x, y) on a closed and bounded domain must occur on the boundary of the domain. Furthermore, it can be easily seen that if the domain is a polygon, then the global minimum and maximum values of f must occur at a vertex of the polygon. Find the global minimum and maximum values of f (x, y) = 4x-8y- 5 on the domain where |x|+|y| ≤ 8. (Give your answers as a whole numbers.) global minimum: global maximum:
Transcribed Image Text:A linear function f (x, y) = ax + by + c has no critical points. Therefore, the global minimum and maximum values of f (x, y) on a closed and bounded domain must occur on the boundary of the domain. Furthermore, it can be easily seen that if the domain is a polygon, then the global minimum and maximum values of f must occur at a vertex of the polygon. Find the global minimum and maximum values of f (x, y) = 4x-8y- 5 on the domain where |x|+|y| ≤ 8. (Give your answers as a whole numbers.) global minimum: global maximum:
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