Re: Re: Can Maximize return a function

• To: mathgroup at smc.vnet.net
• Subject: [mg74951] Re: [mg74905] Re: Can Maximize return a function
• From: Daniel Huber <dh at metrohm.ch>
• Date: Thu, 12 Apr 2007 04:54:34 -0400 (EDT)
• References: <evd3qo\$5h2\$1@smc.vnet.net> <200704101003.GAA10297@smc.vnet.net> <F8AF539D-7A7F-403C-94E1-2E366C1E6B6D@mimuw.edu.pl>

```Hi Andrzej,
thank's for showing this usage of ForAll to me. I noted that ForAll can
deal with a being a symbols and rational number, but not with reals or
computer numbers. Is there a deeper reason for this? E.g. that division
is not well defined in this domain?
Andrzej Kozlowski wrote:
> *This message was transferred with a trial version of CommuniGate(tm)
> Pro*
> Or you can do it purely algebraically (without finding critical points):
>
> f[x_] := a*x - x^2
>
> Resolve[ForAll[x, x â?? Reals, f[x] <= f[b]], b]
>
> a â?? Reals && b == a/2
>
>
> Andrzej Kozlowski
>
>
> On 10 Apr 2007, at 19:03, dh wrote:
>
>>
>>
>> Hi,
>>
>> No Maximize can not work symbolically. However, you may e.g. use Reduce
>>
>> or Solve to serach for singular points where the derivative is zero.
>> E.g.:
>>
>> Reduce[{D[a*x-x^2,x]==0},x]
>>
>> Daniel
>>
>>
>>
>>
>>> e.g.
>>
>>>
>>
>>> When I run:
>>
>>>
>>
>>> Clear["*"]
>>
>>> SetAttributes[a, Constant]
>>
>>> (*this works if use a num instead of a*)
>>
>>> (*e.g. f[x_] := 4*x - x^2 *)
>>
>>> f[x_] := a*x - x^2
>>
>>> Maximize[f[x], a > 0, x]
>>
>>>
>>
>>> I get:
>>
>>>
>>
>>> Maximize[{-x^2+xy, y>0},x]
>>
>>>
>>
>>> when I really want something like:
>>
>>>
>>
>>> {a, {x->a/2}}
>>
>>>
>>
>>> Can this be done?
>>
>>>
>>
>>>
>>
>>
>>
>
>
>

--

Daniel Huber
Metrohm Ltd.
Oberdorfstr. 68
CH-9100 Herisau
Tel. +41 71 353 8585, Fax +41 71 353 8907
E-Mail:<mailto:dh at metrohm.ch>
Internet:<http://www.metrohm.ch>

```

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