       Re: Problem finding maximum

• To: mathgroup at smc.vnet.net
• Subject: [mg127583] Re: Problem finding maximum
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Sun, 5 Aug 2012 02:34:51 -0400 (EDT)
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• References: <20120805014915.A5ED5684F@smc.vnet.net>

```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?
>

```

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