Apark ranger has 32 feet of fencing to fence four sides of a rectangular recycling site. what is the greatest area of recycling site that the ranger can fence? explain how you know.

Step-by-step explanation:

The formulas for the perimeter and area of the rectangle are, respectively:

After some algebraic handling, the formula for area is simplified into the following form:

The maximum area is found by means of First and Second Derivative Tests:

According to the second derivative, the critical point leads invariantly to an absolute maximum. The value of the critical point is:

The length of the other side is:

The maximum area of the recycling site is:

c: lkllmn.

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