Use Lagrange multipliers to prove that the rectangle with maximum area that has a given perimeter p is a square. Let the sides of the rectangle be x and y and let f and g represent the area (A) and perimeter (p), respectively. Find the fo A = f(x, y) = p = g(x, y) = V(x, y) = AVg = Then i = implies that x = Therefore, the rectangle with maximum area is a square with side length

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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Use Lagrange multipliers to prove that the rectangle with maximum area that has a given perimeter p is a square.
Let the sides of the rectangle be x and y and let f and g represent the area (A) and perimeter (P), respectively. Find the following.
A = f(x, y) =
p = g(x, y) =
V(x, y) =
AVg =
Then i =
implies that x =
Therefore, the rectangle with maximum area is a square with side length
Transcribed Image Text:Use Lagrange multipliers to prove that the rectangle with maximum area that has a given perimeter p is a square. Let the sides of the rectangle be x and y and let f and g represent the area (A) and perimeter (P), respectively. Find the following. A = f(x, y) = p = g(x, y) = V(x, y) = AVg = Then i = implies that x = Therefore, the rectangle with maximum area is a square with side length
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