Re: help in question on differentiable

From: José Carlos Santos <jcsantos@xxxxxxxx>
Date: Thu, 27 Sep 2007 15:30:52 +0100

On 27-09-2007 15:08, tomas wrote:

let f:RXR->R be differentiable.
For each x in R define g_x:R->R by g_x(y)=f(x,y)
suppose that for each x there is unique y with
g_x'(y)=0 ,
let c(x) be this y.
IF D22_f(x,y) not equal to zero for all (x,y) show that c
is differentiable .

Done.

Any more requests?

which thereom should I use?

The implicit function theorem.

Best regards,

Jose Carlos Santos
.

Follow-Ups:
- Re: help in question on differentiable
  - From: The World Wide Wade

References:
- help in question on differentiable
  - From: tomas
- Re: help in question on differentiable
  - From: José Carlos Santos
- Re: help in question on differentiable
  - From: tomas

Prev by Date: Re: Godel's proof, truth, reality, self-awareness, and all that jazz
Next by Date: Re: Two results of set geometry
Previous by thread: Re: help in question on differentiable
Next by thread: Re: help in question on differentiable
Index(es):
- Date
- Thread

Relevant Pages

Re: A question on Reimann (ref Prime Obsession by John Derbyshire)
... zero. ... Best regards, ... Jose Carlos Santos ... It is a book written for non-mathematicians like me so I expect you ...
(sci.math)
Re: three identity
... words, if I speak about the "canonical base" of ell^2, then people ... th component is 1 with all other equal to zero? ... Best regards, ... Jose Carlos Santos ...
(sci.math)
Re: sin(1/x)
... Imagine the graph first. ... It is infinitely oscillated near zero, ... Best regards, ... Jose Carlos Santos ...
(sci.math)
Re: help in question on differentiable
... IF D22_fnot equal to zero for all show that c ... Best regards, ... Jose Carlos Santos ... which thereom should I use? ...
(sci.math)
Re: Algebra - Prove > 0
... bigger than zero? ... Best regards, ... Jose Carlos Santos ...
(sci.math)