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
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f142c6f-c47b-48e7-a067-043e41a4d516%2F93be582f-6879-463d-b192-ad007b0ec3cc%2Fb3nzmoq_processed.png&w=3840&q=75)
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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