A stick of length L is broken into n equal parts.

What is the maximal product of their lengths?

(In reply to

re(2): What Ady wants (spoiler?) by Daniel)

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**