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August 4th, 2019, 12:28 PM   #1
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Minimal value

Find the minimal value of $\displaystyle f(x)=e^{x} +|x|\cdot e^{x} .$

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August 4th, 2019, 01:12 PM   #2
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$f(x)\gt 0$ for all $x$. $f(x)\to 0$ as $x\to -\infty$. That is the minimum.
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August 4th, 2019, 07:14 PM   #3
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Isn't 0 a limiting value (and greatest lower bound) rather than a minimum value?
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August 5th, 2019, 12:34 PM   #4
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It depends on a precise definition of minimum. Greatest lower bound is precise, minimum is not.
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August 5th, 2019, 11:57 PM   #5
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Quote:
Originally Posted by mathman View Post
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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