Of all rectangles with a perimeter of 20, which one has the maximum area? ... If x and y are the length and width of the rectangle, respectively, then the area of the rectangle is A = xy, Writing the area function as a function of x, it follows that the area is A(x) = Evaluate A at the endpoints of and at the critical point of A. It follows that A where 2x + 2y = where ≤x≤ has an absolute maximum value at x = length of and a width of (Simplify your answers.) . Therefore, the rectangle that has the maximum area has a
Of all rectangles with a perimeter of 20, which one has the maximum area? ... If x and y are the length and width of the rectangle, respectively, then the area of the rectangle is A = xy, Writing the area function as a function of x, it follows that the area is A(x) = Evaluate A at the endpoints of and at the critical point of A. It follows that A where 2x + 2y = where ≤x≤ has an absolute maximum value at x = length of and a width of (Simplify your answers.) . Therefore, the rectangle that has the maximum area has a
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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Of all rectangles with a perimeter of 20, which one has the maximum area?
If x and y are the length and width of the rectangle, respectively, then the area of the rectangle is
A=xy,
where
2x+2y=enter your response here.
Writing the area function as a function of x, it follows that the area is
A(x)=enter your response here,
where
enter your response here≤x≤enter your response here.
Evaluate A at the endpoints of
enter your response here,enter your response here
and at the critical point of A. It follows that A has an absolute maximum value at
x=enter your response here.
Therefore, the rectangle that has the maximum area has a length of
enter your response here
and a width of
enter your response here.
Transcribed Image Text:Of all rectangles with a perimeter of 20, which one has the maximum area?
If x and y are the length and width of the rectangle, respectively, then the area of the rectangle is A = xy,
where 2x + 2y =. Writing the area function as a function of x, it follows that the area is A(x) =
where ≤x≤ Evaluate A at the endpoints of
and at the critical point of A. It follows that A
Therefore, the rectangle that has the maximum area has a
has an absolute maximum value at x =
length of and a width of
(Simplify your answers.)
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