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Re: parameter restrictions
*To*: mathgroup at smc.vnet.net
*Subject*: [mg32442] Re: [mg32428] parameter restrictions
*From*: "soso lala" <sosolala at hotmail.com>
*Date*: Mon, 21 Jan 2002 02:54:53 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
Hi
Thanks for your answer. Unfortunately, it does not work like this. Consider
the following example:
Clear[f,x,a,b]
f[x_,a_,b_]:= -x^(a+b)
The second derivation with respect to x is:
D[f[x,a,b],{x,2}]
-(-1+a+b)(a+b)x^(-2+a+b)
Given that x>0,a>0,b>0 and (a+b)<1 this derivation is unambiguously
positive. I have tried to show this with Mathematica in the manner proposed:
Clear[f,x,a,b]
f[x_?Positive,a_?Positive,b_?Positive]:= -x^(a+b) /; (a+b)<1
Now, if I write
D[f[x,a,b],{x,2}]>0
I would expect the output
TRUE
but I receive
f^(2,0,0)[x,a,b]>0
Can somebody tell me where the mistake is or how I must define parameter
restrictions?
Thanks for your efforts
Jack
>From: BobHanlon at aol.com
To: mathgroup at smc.vnet.net
>Subject: [mg32442] Re: [mg32428] parameter restrictions
>Date: Sat, 19 Jan 2002 20:47:10 EST
>
>
>In a message dated 1/19/02 8:05:36 PM, sosolala at hotmail.com writes:
>
> >I am using Mathematica 4.0 and have a question about parameter
>restrictions.
> >
> >How can I define the range of values of a parameter, e.g. that alpha must
> >be
> >positive or that (alpha + beta) must be less than unity?
> >
> >Although it may be a very simple question (and/or answer) I would be
> >delighted if I get an answer.
> >
>
>f[x_, a_?Positive] := a*x;
>
>f[x_, a_?Positive, b_?NonNegative] := a^x*b /; (a+b) < 1;
>
>
>Bob Hanlon
>Chantilly, VA USA
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