FindMaximum with constraints, WorkingPrecision issue

Questions
1

Hello,

do you know why the error message in the following example appears? Somehow it appears when introducing the constraint x>0…

In[60]:= FindMaximum[{x - 2 x^2, x > 0}, x, WorkingPrecision -> 8]

SetPrecision::precsm: Requested precision 8.` is smaller than $MinPrecision. Using $MinPrecision instead. >>

SetPrecision::precsm: Requested precision 8.` is smaller than $MinPrecision. Using $MinPrecision instead. >>

Out[60]= {0.12499999, {x -> 0.2500719625311951}}

I am using Mathematica 9, my OS is Ubuntu with 64 bit.

Thank you in advance,
Igor

2

ok I found the solution myself:

In[12]:= FindMaximum[{x - 2 x^2 && x > 0}, x,
WorkingPrecision → 8]

Out[12]= {0.12500000, {x → 0.24995000}}

(that is && insted of ,)

However still I am wondering what made the difference and why with Maximize the “,” works and not the “&&”

In[13]:= Maximize[{x - 2 x^2 && x > 0}, x, WorkingPrecision → 8]

Out[13]= Maximize[{x - 2 x^2 && x > 0}, x, WorkingPrecision → 8]

In[6]:= Maximize[{x - 2 x^2, x > 0}, x, WorkingPrecision → 8]

Out[6]= {1/8, {x → 1/4}}