Re: How can I use FindMaximum to get a result better than

• To: mathgroup at smc.vnet.net
• Subject: [mg127964] Re: How can I use FindMaximum to get a result better than
• From: Dana DeLouis <dana01 at me.com>
• Date: Thu, 6 Sep 2012 04:12:14 -0400 (EDT)
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> Then played around to try to get a more accurate result.
> In[9]:= FindMaximum[8 E^(-x) Sin[x] -1,{x,0,8},AccuracyGoal->20, PrecisionGoal->20]

> Out[9]= {1.57918, {x -> 0.785398}}
> Any suggestions?

Hi.  Here are two suggestions:

equ = 8 E^(-x) Sin[x]-1 ;

// Full Precision:

Maximize[{equ,0<x<1},x,Reals]  //FullSimplify

{-1 + (4*Sqrt[2])/E^(Pi/4),  {x -> Pi/4}}

%//N
{1.57918,{x->0.785398}}

// The old derivative trick:

Solve[D[equ,x]==0,x]  //Quiet
{{x -> Pi/4}}

= = = = = = = = = =
HTH   :>)
=E2=80=A8Dana DeLouis
=E2=80=A8= = = = = = = = = =

On Tuesday, September 4, 2012 5:50:53 AM UTC-4, David Kirkby wrote:
> I've tried this:
>
>
>
> In[2]:= FindMaximum[8 E^(-x) Sin[x] -1,{x,0,8}]
>
>
>
> Out[2]= {1.57918, {x -> 0.785398}}
>
>
> Then played around to try to get a more accurate result.
>
>
>
> In[9]:= FindMaximum[8 E^(-x) Sin[x] -1,{x,0,8},AccuracyGoal->20, PrecisionGoal->20]
>
>
>
> Out[9]= {1.57918, {x -> 0.785398}}
>
>
>
> In[10]:= Precision[%]
>
>
> Also:
>
> In[7]:= N[FindMaximum[8 E^(-x) Sin[x] -1,{x,0,8},AccuracyGoal->200, PrecisionGoal->200],100]
>
>
>
> Out[7]= {1.57918, {x -> 0.785398}}
>
> In[8]:= Precision[%]
>
> Out[8]= MachinePrecision
>

> Any suggestions?

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