Needed; ( a woman wants to build a rectangular garden. she plans to use a side of a shed for one side of the garden. she has 84 yards of fencing material.

what is the maximum area that will be enclosed?

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Let x denote the length of the side of the garden which is covered fenced by a shed, and be the width of the garden.

The perimeter of a rectangle is given by 2(length + width).
Given that on of the sides is to be covered by the side of a shed, the the perimeter of the remaining three sides to be fenced is given by

which gives:

For the area to be maximum, the differentiation of A with respect to x must be equal to 0.
i.e.
Therefore, the maximum area of the garden enclosed is given by