*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