How can I use FindMaximum to get a result better than MachinePrecision?

• To: mathgroup at smc.vnet.net
• Subject: [mg127940] How can I use FindMaximum to get a result better than MachinePrecision?
• From: David Kirkby <drkirkby at gmail.com>
• Date: Tue, 4 Sep 2012 05:45:26 -0400 (EDT)
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```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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