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A simple use of Calculus

A simple use of Calculus

You're fencing in a rectangular garden against a wall. So no fence is needed along the wall.

You have 100 feet of fencing. What size do you make the garden to maximize its area?

Let the garden be y deep and x wide.

So its area is a=xy

The length of fencing is l=2y+x=100

So x=100-2y

Substitute this into the area, so a=y(100-2y)=100y-2y^2

Differentiate and set to zero to find the max..


So y=25

Which means the garden is 25 deep and 50 wide.

Content written and posted by Ken Abbott
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