suppose you are enclosing a rectangular area to create a rabbit cage. you have 80 ft of fence and want to build a pen with the largest possible area for your rabbit, so you build the cage using an existing building as one side.

Question

make a table showing the areas for some selected values of x, and write a function that gives the area, y, as a function of the width, x

Answer 1

Let x be the width of the side parallel to the building. The other two sides then have length (80-x)/2

The area is y = x(40 - x/2)
y = 40x - (x^2/2)

You get maximum area when dy/dx = 0
40 -x = 0
x = 40

Table:
x y
20 600
30 750
39 799.5
40 800
41 799.5
50 750
60 600

Answer 2

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