**Mail Archives: djgpp/1997/12/14/19:33:06**
Benjamin F. Keil wrote:
>
> A. Sinan Unur wrote:
> >
> > Paul Derbyshire wrote:
> > <SNIP>
> > > you're in deep doodoo), or a certain editor-cum-operating-system I
> > > shall not name, which has a learning curve like e^x and a manual
> > > the size of a phone book and half as well organized ;-)
> >
> > that is supported by neither theory nor fact. it is not supported by
> > fact, because people do learn it. a learning curve such as e^x means
> > there will never be any learning. theoretically, for the concept of
> > 'learning curve' to have any meaning, the function should probably
> > be strictly increasing and concave.
>
> e^x fits that description. e^x is everywhere increasing and has
> upwards concavity.
i know this is off-topic, but i hate seeing my supposedly humorous
responses ruined this way ;-) send flames by e-mail please.
a twice differentiable function is said to be (strictly) concave if its
second derivative is (negative) nonpositive, and (strictly) convex
(which is what you are calling 'upwards concavity') if its second
derivative is (positive) nonnegative.
--
----------------------------------------------------------------------
A. Sinan Unur
Department of Policy Analysis and Management, College of Human Ecology,
Cornell University, Ithaca, NY 14853, USA
mailto:sinan DOT unur AT cornell DOT edu
http://www.people.cornell.edu/pages/asu1/

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