Multi-compartment model: Difference between revisions

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[[File:Steiner problem.svg|right|300px]]
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'''Steiner's problem''' is the problem of finding the [[maxima and minima|maximum]] of the [[function (mathematics)|function]]
 
: <math>f(x)=x^{1/x}.\,</math><ref>{{cite web
| url = http://mathworld.wolfram.com/SteinersProblem.html
| title = Steiner's Problem
| author = Eric W. Weisstein
| publisher = MathWorld
| accessdate = 12/08/2010
}}</ref>
 
It is named after [[Jakob Steiner]].
 
The maximum is at <math>x=e</math>, where ''e'' denotes the [[e (mathematical constant)|base of natural logarithms]]. One can determine that by solving the equivalent problem of maximizing
 
: <math>g(x)=\ln f(x) = \frac{\ln x}{x}.</math>
 
The [[derivative]] of <math>g</math> can be calculated to be
 
: <math>g'(x)= \frac{1-\ln x}{x^2}.</math>
 
It follows that <math>g'(x)</math> is positive for <math>0<x<e</math> and negative for <math>x>e</math>, which implies that <math>g(x)</math> (and therefore <math>f(x)</math>) increases for <math>0<x<e</math> and decreases for <math>x>e.</math> Thus,  <math>x=e</math> is the unique global maximum of <math>f(x).</math>
 
==References==
<references />
 
{{DEFAULTSORT:Steiner's Problem}}
[[Category:Functions and mappings]]
[[Category:Mathematical optimization]]

Revision as of 06:19, 17 February 2014

The person who wrote the post is known as Jayson Hirano and he totally digs that name. Invoicing is what I do for a residing but I've always wanted my own business. Her family life in Ohio but her husband desires them to transfer. My husband doesn't like it the way I do but what I really like performing is caving but I don't have the time lately.

My web page; psychics online

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