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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

> 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?