Respuesta :
The equation for the area in terms of x gives the function David should
use to maximize the area.
Response:
The equation that David should use to help him maximize the area is option A.
- A. f(x) = x·(400 - 2·x)
How can the function for the area be obtained?
The given parameter are;
Length of fencing David has = 400 yards
Area to be enclosed = Rectangular area with pre-existing fence (on one side)
Required:
The equation David should use to maximize the area.
Solution:
Let x represent the width of the area (the sides perpendicular to the pre-
existing fence), and let y represent the length of pre-existing fence
We have;
Length of fencing available = Opposite side to pre-existing fence + 2 × Width of the area
Opposite side to pre-existing fence = Length of pre-existing fence
Which gives;
Length of fencing available = Length of pre-existing fence + 2 × Width of the area
400 = y + 2·x
y = 400 - 2·x
Area = Length × Width
Which gives;
Area = y × x
Area as a function of x is therefore;
Area, f(x)= (400 - 2·x) × x
Which gives;
- f(x) = x·(400 - 2·x)
The correct option is therefore;
- A. f(x) = x·(400 - 2·x)
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