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Calculus Level 3

For \(2<x<5\), the greatest value of \((5-x)^{2}(x-2)^{5}\) is at \(x=\dfrac{a}{b}\), where \(a,b\) are coprime integers.

Enter value of \(ab\) as your answer.


You can try my other Sequences And Series problems by clicking here : Part II and here : Part I.
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