Use the method of Lagrange multipliers to prove that the rectangular box with maximum volume that has a fixedsurface area S must be a cube.

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.
Chapter8: Further Techniques And Applications Of Integration
Section8.3: Volume And Average Value
Problem 25E
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Use the method of Lagrange multipliers to prove that the rectangular box with maximum volume that has a fixed
surface area S must be a cube.

 

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