SOLUTION: Suppose a farmer has 1000m of fencing to enclose a rectangular field. What is the largest area that the farmer can enclose?

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The Perimeter is:




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The Area is:



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First of all, when the coefficient of the
squared term is negative, then there is a maximum
and not a minimum.
When the equation is in the form
, the max or min is
always at , or, in this case,


and I know that



The largest area that the farmer can enclose
is = 62,500 ft2
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I can prove this by changing the dimensions
slightly, but still keeping the same Perimeter
= 62,499 ft2
= 62,496 ft2 ( even less )