Wikipedia:Reference desk/Archives/Mathematics/2011 February 26

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February 26

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Lagrangian Multipliers

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I'm having some difficulties with using Lagrangian multipliers correctly, and would appreciate any help anyone can give. I thought I'd start with a simple problem that I can easily check the answer to, but I can't get the right answer. In particular, what is the largest volume of cube that will fit inside a unit sphere? My attempted solution is below.

 
 
 

Hence:

 
 
 
 

Using Wolfram Alpha to solve the simultaneous equations, to prevent me from messing that bit up, I get the following (ignoring non-physical negative solutions): :  This is obviously not correct. Where have I gone wrong? --131.111.184.8 (talk) 21:31, 26 February 2011 (UTC) Please ignore the above, I've just realised what I've done... (for the interested, side length is twice x...) --131.111.184.8 (talk) 21:35, 26 February 2011 (UTC)[reply]

  Resolved

StuRat (talk) 00:55, 1 March 2011 (UTC)[reply]