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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.