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\medskip \begin{center}{\bf Problem No. 1270, Elemente der Mathematik No. 4/2008\\
Proposed by Vicen\c{t}iu R\u{a}dulescu\\ Institute of Mathematics ``Simion Stoilow" of the Romanian Academy \\ \& \\Department of
Mathematics,
University of Craiova, 200 585 Craiova, Romania\\ E-mail: {\tt
vicentiu.radulescu@math.cnrs.fr}\quad
{\tt http://inf.ucv.ro/$\sim$radulescu}}\end{center}

\bigskip
{\it
Prove that there does not exist a positive twice differentiable function
$f$ defined on $[0,\infty)$ such that $f(x)f''(x)+1\leq 0$ for all $x\geq 0$.}

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