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Let's say that we have function $u:\mathbb R_0\to \mathbb R$ with $u'(x)>0$, $u''(x)<0$, $u'''(x)>0$, $\lim_{x\to 0} u'(x) = \infty, \lim_{x\to 0}u'(x) = 0$.

Take $x_1 < x_2$. Does $$\frac{u'''(x_1)}{u'''(x_2)}\leq \frac{u'(x_1)}{u'(x_2)}$$ always hold?

Thanks, I'm lost here.

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    What do you mean by R_0?2012-11-14
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    ... and how can $\lim_{x \to 0} u'(x)$ be both "inf" (I assume $\infty$ and $0$?2012-11-14
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    I would guess that this is from the positive reals to the reals and the second limit is as $x \to \infty$2012-11-14
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    For some basic information about writing math at this site see e.g. [here](http://meta.math.stackexchange.com/questions/5020/), [here](http://meta.stackexchange.com/a/70559/155238), [here](http://meta.math.stackexchange.com/questions/1773/) and [here](http://math.stackexchange.com/editing-help#latex).2012-11-14

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