The curve is .

Generate the area function of the rectangle that can be inscribed under the curve.

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Observe the graph:

Since the curve is symmetric about axis, then the length will be .

Breadth will be the value of the function.

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Substitute and in .

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Differentiate on each side with respect to . 

For the maximum area of the rectangle, .

Area of the rectangle is maximum when .

If then .

Graph the curve with inscribed rectangle. 

Therefore, area of the largest rectangle is

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