|
| Author |
Message |
|
Koala
Frequent VisitorJoined: 07 Mar 2004Posts: 36
|
|
Posted: Sun Feb 06, 2005 3:53 pm Post subject: condition for single-variable Inverse Function Theorem
|
|
|
|
Let be strictly monotonic on , differentiable at , and .
Is it true that is differentiable at ?
|
|
|
|
|
|
Andy
Frequent VisitorJoined: 28 Oct 2003Posts: 391
Location: Hong Kong
|
|
Posted: Sun Feb 06, 2005 4:29 pm Post subject:
|
|
|
|
Yes. For convenience, let the inverse of f be g and f(0) = c.
As f is monotone near 0, holds when y is close to c. Therefore, we have
_________________
Patience and tolerance are necessarily demanded Year-round.
|
|
|
|
|
|
Koala
Frequent VisitorJoined: 07 Mar 2004Posts: 36
|
|
Posted: Sun Feb 06, 2005 6:05 pm Post subject:
|
|
|
|
Thank you Andy. I should be more precise by asking in this way:
Is always an interior point of the domain of ?
|
|
|
|
|
|
|
|
All times are GMT + 8 Hours
|
|
| |
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum
|
|
