Possible proof a Global Min?
- To: mathgroup@smc.vnet.net
- Subject: [mg10696] Possible proof a Global Min?
- From: Ersek_Ted%PAX1A@mr.nawcad.navy.mil
- Date: Fri, 30 Jan 1998 04:24:32 -0500
In the lines below I use Plot, FindMinimum and then Rationalize to
convince myself that;
BesselJ[4,x] > -(63899/315140) for (11< x <30)
Is it possible to prove that this is true? If so can you give me some
idea how it is done. If it is possible it would be great if the same
approach can be used for many other functions involving elementary
functions, special functions, etc.
In[1]:=
Plot[BesselJ[4,x],{x,11,30}]
Out[1]=
-Grahpics not shown-
In[2]:=
fmin=FindMinimum[BesselJ[4,x],{x,16}] [[1]]
Out[2]=
-0.202764
In[3]:=
lowest=Rationalize[fmin-10^-12, 10^-11]
Out[3]=
-(63899/315140)
In[4]:=
lowest<fmin
Out[4]=
True