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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) = Vf(x, y) = λVg = 1²/²y = Then λ = implies that x = Therefore, the rectangle with maximum area is a square whose side length in terms of p is

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) = Vf(x, y) = λVg = 1²/²y = Then λ = implies that x = Therefore, the rectangle with maximum area is a square whose side length in terms of p is

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.9: Properties Of Determinants
Problem 46E
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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) = Vf(x, y) = = XVg = Then ==y= = ²/²y = implies that x = Therefore, the rectangle with maximum area is a square whose side length in terms of p is
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) = Vf(x, y) = = XVg = Then ==y= = ²/²y = implies that x = Therefore, the rectangle with maximum area is a square whose side length in terms of p is
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