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2. Show that among all rectangles, the square has the minimum perimeter. Let the objective function be the perimeter: P = 2x + 2y and let the area "A" be A = ry. [HINT: You need to first use the two functions to get the perimeter function in terms of one variable. Then find the derivative of it, to find the critical value. Then use either test for derivatives (first or second), to see if there is in fact a minimum at the critical value obtained. Finally, you must prove that z = y, since this shows that the rectangle is in fact a square.] See the diagrams below. X Rectangle Square+y Where

2. Show that among all rectangles, the square has the minimum perimeter. Let the objective function be the perimeter: P = 2x + 2y and let the area "A" be A = ry. [HINT: You need to first use the two functions to get the perimeter function in terms of one variable. Then find the derivative of it, to find the critical value. Then use either test for derivatives (first or second), to see if there is in fact a minimum at the critical value obtained. Finally, you must prove that z = y, since this shows that the rectangle is in fact a square.] See the diagrams below. X Rectangle Square+y Where

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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2. Show that among all rectangles, the square has the minimum perimeter. Let the objective function be the perimeter: P = 2x + 2y and let the area "A" be A = xy. [HINT: You need to first use the two functions to get the perimeter function in terms of one variable. Then find the derivative of it, to find the critical value. Then use either test for derivatives (first or second), to see if there is in fact a minimum at the critical value obtained. Finally, you must prove that a = y, since this shows that the rectangle is in fact a square.] See the diagrams below. X y Rectangle Square- Where x = y
Transcribed Image Text:2. Show that among all rectangles, the square has the minimum perimeter. Let the objective function be the perimeter: P = 2x + 2y and let the area "A" be A = xy. [HINT: You need to first use the two functions to get the perimeter function in terms of one variable. Then find the derivative of it, to find the critical value. Then use either test for derivatives (first or second), to see if there is in fact a minimum at the critical value obtained. Finally, you must prove that a = y, since this shows that the rectangle is in fact a square.] See the diagrams below. X y Rectangle Square- Where x = y
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