Re: Re: Can Maximize return a function

• To: mathgroup at smc.vnet.net
• Subject: [mg74926] Re: [mg74905] Re: Can Maximize return a function
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Wed, 11 Apr 2007 02:02:15 -0400 (EDT)
• References: <evd3qo\$5h2\$1@smc.vnet.net> <200704101003.GAA10297@smc.vnet.net>

```Or you can do it purely algebraically (without finding critical points):

f[x_] := a*x - x^2

Resolve[ForAll[x, x =E2=88=88 Reals, f[x] <= f[b]], b]

a =E2=88=88 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?
>
>>
>
>>
>
>
>

```

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