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A local garden store plans to build a large rectangular sign on the interior wall at one end of their greenhouse. The roof along this wall is centered around a vertical support beam. The height of the roof, r (measured in meters), can be expressed as a function the horizontal distance from the vertical support beam, x (measured in meters), by r(x) = 5 -* - 4

A local garden store plans to build a large rectangular sign on the interior wall at one end of their greenhouse. The roof along this wall is centered around a vertical support beam. The height of the roof, r (measured in meters), can be expressed as a function the horizontal distance from the vertical support beam, x (measured in meters), by r(x) = 5 -* - 4

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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A local garden store plans to build a large rectangular sign on the interior wall at one end of their greenhouse. The roof along this wall is centered around a vertical support beam. The height of the roof, r (measured in meters), can be expressed as a function the horizontal distance from the vertical support beam, x (measured in meters), by r(x) = 5 -* - 4 <x< 4 This curve is graphed to the right; the shaded rectangle is one possible sign that could be built. The store wants to create the largest sign it can. -4 a. Write the area A(x) of the sign (in square meters), as a function of x, Be sure to specify the domain of A(x). b. Find the value(s) of x for which the sign has the largest possible area. Use calculus to find your answers, and be sure to show enough evidence that the values you find do in fact maximize the area.
Transcribed Image Text:A local garden store plans to build a large rectangular sign on the interior wall at one end of their greenhouse. The roof along this wall is centered around a vertical support beam. The height of the roof, r (measured in meters), can be expressed as a function the horizontal distance from the vertical support beam, x (measured in meters), by r(x) = 5 -* - 4 <x< 4 This curve is graphed to the right; the shaded rectangle is one possible sign that could be built. The store wants to create the largest sign it can. -4 a. Write the area A(x) of the sign (in square meters), as a function of x, Be sure to specify the domain of A(x). b. Find the value(s) of x for which the sign has the largest possible area. Use calculus to find your answers, and be sure to show enough evidence that the values you find do in fact maximize the area.
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