Split a number into n parts and multiply them.How much parts should you split(to get large product)?

$$(\frac{1}{n})^n=n^{-n}$$

$$n^{-n}\frac{d}{dn}=????$$

I know how to do $$n^c\frac{d}{dn}=cn^{c-1}$$ or $$c^n\frac{d}{dn}=c^n\ln c$$

(yeah ik it has a d/dn===0 point at n=e but i dont want to copy answers)

trial and errored it out:(ln(x)+1)*(-x^-x)

then solve for (ln(x)+1)(-x^-x)=0

you can make the right part (-x) zero:

(ln(x)+1)(0^0)=indeterminiate

whoops

left part (lnx=-1):

(ln(1/e)+1)(1/e^1/e)=(1-1)(some_weird_transcedental)=0

Conclusion:2 roots,x=0 and x=1/e

meaning that you either break the number into 0 parts and explode the calculator or break it making each part close to e

Umm, first, you put this in the wrong category (help with Snap*!*).

But also, yes, we're happy to have occasional non-Snap*!*-related threads here, that doesn't mean you should give us a calculus tutorial. There are other places for that.

Thanks.

Oops

(thank u i was just going to change the category)

This topic was automatically closed 30 days after the last reply. New replies are no longer allowed.