how to prove that f^2+f ' ^2 <=1 if ...

From: eric detourre (eric.detourre_at_laposte.net)
Date: 08/19/04 

Date: Thu, 19 Aug 2004 12:08:45 +0000 (UTC)

Here is the following problem :

Prove that : f^2 + f ' ^2 <= 1 when f is twice differentiable over R and : f^2 <= 1 and : f ' ^2 + f " ^2 <= 1 (1 is greater than the sum of the squre of the first and seconf derivative of f).

I don't have the slightest idea on how to assert this, and this result (which happened to be an exercise in a french engineering school) may be false (but i found no counter-example) as it is false when replacing R with any subset of R.

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