5. We consider a function $h$ defined on $]0; +\infty[$ whose second derivative is defined on $]0; +\infty[$ by:

$$h''(x) = x\ln x - 3x$$

Statement 5: The function $h$ is convex on $[\mathrm{e}^3; +\infty[$.

\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{APPENDIX Exercise 3.}
  \includegraphics[alt={},max width=\textwidth]{e2ce19bd-34ff-4618-8855-c4553a3562a2-9_1712_1468_276_239}
\end{center}
\end{figure}