Greatest possible rectangle

Calculus Level 4

A rectangle has one of its bases on \(y=0\) and is contained between \(x=3\) and \(x=-1\). It's opposite base has two of its points on the graph of \(y=x^3-2x^2+1\) with \(y>0\). Find the perimeter of the rectangle with the greatest possible area that fits the above definition.

Adopted from one of Michael Mendrin's problems.
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