Putnam Problem of the Day

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Putnam Problem of the Day http://math.harvard.edu/putnam(...) !!84u21X0KjW+ Thu Apr 18 08:32:57 2019 No.10569073 [Reply] [Original]

[math]\boxed{
\text{Let }f\text{ be a real function with a continuous third derivative such that}
\\
f(x), f'(x), f''(x), f'''(x)\text{ are positive for all }x\text{. Suppose that }f'''(x)\leq f(x)
\\
\text{for all }x\text{. Show that }f'(x)<2f(x)\text{ for all }x\text{.}
}[/math]

>>	http://math.harvard.edu/putnam(...) !!84u21X0KjW+ Thu Apr 18 08:33:55 2019 No.10569076 Previous Thread >>10566116

>>	Anonymous Thu Apr 18 09:06:25 2019 No.10569166 bro please can we get the prismrivers

>>	Anonymous Thu Apr 18 10:34:24 2019 No.10569366 Just glancing at this, do we use Poincare inequality?

>>	Anonymous Thu Apr 18 11:40:34 2019 No.10569516 >>10569073 Thinly veiled intro analysis thread

>>	Anonymous Thu Apr 18 11:44:39 2019 No.10569520 >>10569516 *analysis homework thread

>>	Anonymous Thu Apr 18 12:09:40 2019 No.10569580 This one was tricky. It's a suboptimal inequality, so you have to add in terms oh the RHS to get what you want. I had to start from the beginning multiple times, as well, then fit the suboptimal inequalities together.

>>	Anonymous Thu Apr 18 23:41:21 2019 No.10571107 How much additional math past calc.3 do I need to learn before I can comprehend the answer to this problem?

>>	Anonymous Fri Apr 19 01:35:34 2019 No.10571270 >>10571107 I solved it (I think) with basic calc rules after playing around for a while this morning. So I'd imagine it's a lower level question, like a 1 or 2.

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