       Re: Problem finding maximum

• To: mathgroup at smc.vnet.net
• Subject: [mg127591] Re: Problem finding maximum
• From: Frank K <fkampas at gmail.com>
• Date: Sun, 5 Aug 2012 14:59:14 -0400 (EDT)
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• References: <20120805014915.A5ED5684F@smc.vnet.net> <jvl4bt\$77r\$1@smc.vnet.net>

```On Sunday, August 5, 2012 2:37:49 AM UTC-4, Bob Hanlon wrote:
> f[x_, a_] = (a^3 - 6 x - a^2 (4 + x) +
>
>      a (2 + 12 x - 4 x^2))/(8 a);
>
>
>
> aa1 = .7481;
>
>
>
> Plot[Abs[f[x, aa1]], {x, 0, aa1}]
>
>
>
> "FindMaximum[f, x] searches for a local maximum in f, starting from an
>
> automatically selected point."
>
>
>
> FindMaximum[{Abs[f[x, aa1]],
>
>   0 <= x <= aa1}, x]
>
>
>
> {0.0317268, {x -> 0.7481}}
>
>
>
> "FindMaximum[f, {x, x0}] searches for a local maximum in f, starting
>
> from the point x = x0."
>
>
>
> FindMaximum[{Abs[f[x, aa1]],
>
>   0 <= x <= aa1}, {x, .1}]
>
>
>
> {0.0540933, {x -> 1.*10^-7}}
>
>
>
> You just needed to give it a better starting value than the default.
>
> Alternatively, use NMaximize
>
>
>
> "NMaximize always attempts to find a global maximum of f subject to
>
> the constraints given."
>
>
>
> NMaximize[{Abs[f[x, aa1]],
>
>   0 <= x <= aa1}, x]
>
>
>
> {0.0540933, {x -> 0.}}
>
>
>
>
>
> Bob Hanlon
>
>
>
>
>
> On Sat, Aug 4, 2012 at 9:49 PM, Cisco Lane <travlorf at yahoo.com> wrote:
>
> > I cannot seem to find the corrrect maximum for the  absolute value of the following function in 0<=x<=aa1
>
> >
>
> > aa1 = .7481
>
> >
>
> > f[x_, a_] = (a^3 - 6 x - a^2 (4 + x) + a (2 + 12 x - 4 x^2))/(8 a)
>
> >
>
> > For example, FindMaximum[{Abs[f[x, aa1]], 0 <= x <= aa1}, x] gives {0.0317268, {x -> 0.7481}}
>
> >
>
> > The correct answer is at x=0, where Abs[f[0,aa1]]=0.0540933 but I have tried every maximization function I can think of and nothing will give me the correct answer. Can anyone help?
>
> >

This calculation can be done symbolically if you convert aa1 into a fraction.

In:= f[x_,a_]=(a^3-6 x-a^2 (4+x)+a (2+12 x-4 x^2))/(8 a)
Out= (a^3-6 x-a^2 (4+x)+a (2+12 x-4 x^2))/(8 a)
In:= aa1=Rationalize[.7481]
Out= 7481/10000
In:= Maximize[{Abs[f[x,aa1]],0<=x<=aa1},x]
Out= {43274639/800000000,{x->0}}
In:= N[%]
Out= {0.0540933,{x->0.}}

```

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