Differentiate twice, check that the second derivative is positive, and integrate back using zero condition at -infinity.
Leonid
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From: A UK-based worldwide e-mail broadcast system mailing list [[log in to unmask]] On Behalf Of Esteban Gonzalez [[log in to unmask]]
Sent: 28 November 2012 19:53
To: [log in to unmask]
Subject: Question
Hi,
I need to demonstrate that U(x) = phi(x) + x*Phi(x) > 0 for all x. This is clearly true for x >= 0. In addition U'(x) > 0 for all x, and thus it is a
strictly increasing function.
It would be sufficient to show, for instance that lim (x-> - infinity) U(x) = 0
Any suggestion ?
Thanks in advance,
Esteban
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