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


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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