An advanced biology student wants to test the effects of a chemical fertilizer versus natural fertilizer, so she plans to divide a rectangular garden in half by running a fence parallel to two of the exterior sides. She has a fixed amount of fencing (36m) and she wants to have fencing around the entire garden in addition to the fence down the middle. Find the maximum area of the natural fertilizer garden.

Step-by-step explanation:

The sides are rectangle is shown in the diagram

The perimeter of the fence will be

Area of the smaller section of the garden

Differentiating with respect to y we get

Equating with zero we get

Double derivative of area

at y = 9 the area is maximum

The sides of the entire garden are and

The maximum area of the natural fertilizer garden is

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