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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