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Sign Query

• To: mathgroup at smc.vnet.net
• Subject: [mg19728] Sign Query
• From: David Ridley <dbr1 at duke.edu>
• Date: Mon, 13 Sep 1999 02:40:58 -0400
• Organization: Duke University, Durham, NC, USA
• Sender: owner-wri-mathgroup at wolfram.com

Hello,

Please excuse my ignorance.  I'm trying to sign a function and wonder how 
to go about making some assumptions.

In general, my problem is as follows:
a=b-c
Sign[a]
I know that b<0 and c>0.  How do I tell Mathematica?

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More specifically, my problem is the following:

focp=(-(1+r)Q1[P]-(1+g)Q2[(1+g)P]+c(1+r)Q1'[P]+c(1+g)Q2'[(1+g)P])
/((1+r)Q1'[P]+(1+g)^2Q2'[(1+g)P])

dpdg=Simplify[D[focp,g]]

Sign[dpdg]

where:
c,g,r,P,Q1,Q2 >0
Q1',Q2'<0
Q1", Q2" ???

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Thank you very much for any help that you might be willing to provide.

Regards,
David Ridley