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

*To*: mathgroup at smc.vnet.net*Subject*: [mg127963] Re: How can I use FindMaximum to get a result better than MachinePrecision?*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Wed, 5 Sep 2012 03:10:50 -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

On 9/4/12 at 5:45 AM, drkirkby at gmail.com (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] >Any suggestions? Try: FindMaximum[8 E^(-x) Sin[x] -1,{x,0,8},WorkingPrecision->25] or whatever you desire. Also note: In[14]:= D[8 E^(-x) Sin[x] - 1, x] Out[14]= (8*Cos[x])/E^x - (8*Sin[x])/E^x Which clearly indicates a minima or maxima occurs when Sin[x] == Cos[x]. Given the result is multiplied by Exp[-x], it is clear you want x to be as small of a positive number as possible to get a maximum. So, the maximum must occur at Pi/4 exactly