Please help me solve this problem:
Question: One-hundred (100) feet of fence is used to fence in a rectangular yard. Find the length and width that give maximum area.
Thanks in advance for your assistance.
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Formula for the area is, .
As ,
So our formula becomes, .
To find the extremum point, we will differentiate it and will give us the extremum point.
There's an extremum point at , but we don't know whether it's a minima or a maxima. The second derivative test will help us to determine what it is
If , then it's a minima. If , it's a maxima.
, which is less than 0 and which makes our point a maxima
So will give us the maximum area.