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 Optimal result (Posted on 2018-06-04)
A stick of length L is broken into n equal parts.

What is the maximal product of their lengths?

 No Solution Yet Submitted by Ady TZIDON No Rating

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 re(3): What Ady wants (spoiler?) | Comment 6 of 11 |

Daniel:

Excellent approaches!  I tried taking the derivative before taking the log, and that of course fails because the derivative of (L/n)^n with respect to n is just (L/n)^n.

There is a math error in your second approach, resulting from a mistake is simplifying one of your equations.  It should say:

for there to be a local max at n=k then we need for L to be in the interval

[k^k/(k-1)^(k-1),(k+1)^(k+1)/k^k]

Your 2nd method works great after this is fixed.

Edited on June 7, 2018, 8:55 am
 Posted by Steve Herman on 2018-06-05 12:36:11

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