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Maximize returning approximate values


Hello.

>From Maximize documentation in V7.0.3:

* Maximize will return exact results if given exact input.

I've tried to maximize n/n! without success:

In[8]:= Maximize[n/n!, n]
Out[8]= Maximize[n/n!, n]

But a Plot shows that the maximum is around 1.5, so I tried:

In[9]:= Maximize[{n/n!, 0 <= n <= 3}, n]
During evaluation of In[9]:= Maximize::nint: Warning: Maximize used
numeric integration to show that the result is a global maximum. >>
Out[9]= {Root[{-#1! + Gamma[1 + #1] PolyGamma[0, 1 + #1] #1 &,
    1.46163214496836234126265954233}]/
  Root[{-#1! + Gamma[1 + #1] PolyGamma[0, 1 + #1] #1 &,
     1.46163214496836234126265954233}]!, {n ->
   Root[{-#1! + Gamma[1 + #1] PolyGamma[0, 1 + #1] #1 &,
     1.46163214496836234126265954233}]}}


It is partially symbolic, partially numeric.
Is it a bug?

Regards.


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