Question

Shenelle has 100100100 meters of fencing to build a rectangular garden. The garden's area (in square meters) as a function of the garden's width xxx (in meters) is modeled by: A(x)=-(x-25)^2+625A(x)=−(x−25) 2 +625A, left parenthesis, x, right parenthesis, equals, minus, left parenthesis, x, minus, 25, right parenthesis, squared, plus, 625 What side width will produce the maximum garden area?

Answer 1

Answer:

25metres

Step-by-step explanation:

Given the area of the garden in terms of the width modeled by the equation A(x) = -(x-25)²+625 where x is the width of the garden. The side with that will produce the maximum garden area is occurs at when d[A(x)]/dx  = 0

Given A(x) = -(x-25)²+625

d[A(x)]/dx  =-2(x-25) + 0

Since d[A(x)]/dx  = 0

-2(x-25) = 0

open the parenthesis

-2x+50 = 0

-2x = 0-50

-2x = -50

Divide both sides by -2;

-2x/-2 = -50/-2

x = 25metres

Therefore the width of the garden that will produce the maximum garden area is 5metres.