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Internet Message Format  |  1992-12-15  |  751 b 
  1. Path: sparky!uunet!usc!rpi!uwm.edu!spool.mu.edu!olivea!charnel!sifon!CC.UMontreal.CA!cazelaig
  2. From: cazelaig@ERE.UMontreal.CA (Cazelais Gilles)
  3. Newsgroups: sci.math
  4. Subject: proof requested
  5. Message-ID: <1992Dec15.145355.11465@cc.umontreal.ca>
  6. Date: 15 Dec 92 14:53:55 GMT
  7. Sender: news@cc.umontreal.ca (Administration de Cnews)
  8. Organization: Universite de Montreal
  9. Lines: 11
  10.  
  11. I would really appreciate if someone could give me a proof of the following
  12. result. A reference which contains the proof would do the same.
  13.  
  14. The problem is: ......
  15.  
  16.  
  17.        let F:B -> R be a continously differentiable function. Where B is
  18.                          n
  19. the closed unit ball in R .
  20.  
  21. Show that:  max{F(x): x in B} - min{F(x): x in B} >= 2min{||F'(z)||: z in B}
  22.