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 August 4th, 2019, 12:28 PM #1 Senior Member   Joined: Dec 2015 From: somewhere Posts: 708 Thanks: 96 Minimal value Find the minimal value of $\displaystyle f(x)=e^{x} +|x|\cdot e^{x} .$ Last edited by idontknow; August 4th, 2019 at 12:39 PM.
 August 4th, 2019, 01:12 PM #2 Global Moderator   Joined: May 2007 Posts: 6,834 Thanks: 733 $f(x)\gt 0$ for all $x$. $f(x)\to 0$ as $x\to -\infty$. That is the minimum. Thanks from idontknow
 August 4th, 2019, 07:14 PM #3 Global Moderator   Joined: Dec 2006 Posts: 21,015 Thanks: 2250 Isn't 0 a limiting value (and greatest lower bound) rather than a minimum value? Thanks from idontknow
 August 5th, 2019, 12:34 PM #4 Global Moderator   Joined: May 2007 Posts: 6,834 Thanks: 733 It depends on a precise definition of minimum. Greatest lower bound is precise, minimum is not. Thanks from idontknow
August 5th, 2019, 11:57 PM   #5
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Quote:
 Originally Posted by mathman It depends on a precise definition of minimum. Greatest lower bound is precise, minimum is not.
My mistake on the question.

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