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 >> >> >> >> mfmad wrote: >> >>> 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>

**References**:**Re: Can Maximize return a function***From:*dh <dh@metrohm.ch>