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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

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.6: Solving Quadratic Equations By Using The Quadratic Formula
Problem 64PFA
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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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