A gardener wants to make a rectangular enclosure using a wall as one side and 120 m of fencing for the other three sides. Express the area in terms of x, and find the value of x that gives the greatest one.
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Answer:
The area of the enclosure is given by A = x(120 - x). To find the value of x that gives the greatest area, we can take the derivative of A with respect to x and set it equal to 0. This gives us:
A' = 120 - 2x = 0
2x = 120
x = 60
Therefore, the greatest area is achieved when x = 60 m.
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