From 674a0496fa5b00d3facb9035398fbe01b5643579 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Wed, 21 Nov 2018 17:04:17 +0100 Subject: [PATCH] =?UTF-8?q?Feat(TESL):=20=20Travail=20autour=20de=20la=20c?= =?UTF-8?q?onvexit=C3=A9?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- PreStSauveur/TESL/Convexite/Annales.pdf | Bin 0 -> 224969 bytes PreStSauveur/TESL/Convexite/Annales.tex | 70 ++++++++++++++++++ .../TESL/Convexite/fig/2018_Guyane_ex4.png | Bin 0 -> 135011 bytes .../Convexite/fig/2018_Liban_ex3_graph.png | Bin 0 -> 95575 bytes 4 files changed, 70 insertions(+) create mode 100644 PreStSauveur/TESL/Convexite/Annales.pdf create mode 100644 PreStSauveur/TESL/Convexite/Annales.tex create mode 100644 PreStSauveur/TESL/Convexite/fig/2018_Guyane_ex4.png create mode 100644 PreStSauveur/TESL/Convexite/fig/2018_Liban_ex3_graph.png diff --git a/PreStSauveur/TESL/Convexite/Annales.pdf b/PreStSauveur/TESL/Convexite/Annales.pdf new file mode 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+ \end{center} + \item $f'(x)$ est égal à 0 sur l'intervalle + \begin{center} + $]-3;-1]$ \hfill + $[0;1]$ \hfill + $[2;3]$ + \end{center} + \item $f$ est convexe sur l'intervalle + \begin{center} + $]-\infty;2]$ \hfill + $]-\infty;0,5]$ \hfill + $[0;4]$ \hfill + $[2;5]$ + \end{center} + \item $f''$ est égal à 0 en + \begin{center} + 0 \hfill 0,5 \hfill 2 \hfill 3,5 + \end{center} + \end{enumerate} + + \end{minipage} +\end{exercise} + +\begin{exercise}[subtitle={Inspiré de Guyane 2018}] + \includegraphics[scale=1.5]{./fig/2018_Guyane_ex4} +\end{exercise} + +\begin{exercise}[subtitle={Inspiré d'Amérique du Nord 2018}] + On appelle fonction \textbf{satisfaction} toute fonction dérivable qui prend ses valeurs entre 0 et 100. Lorsque la fonction \textbf{satisfaction} atteint la valeur 100, on dit qu’il y a \textbf{saturation}. On définit aussi la fonction \textbf{envie} comme la fonction dérivée de la fonction \textbf{satisfaction}. On dira qu’il y a \textbf{souhait} lorsque la fonction \textbf{envie} est positive ou nulle et qu’il y a \textbf{rejet} lorsque la fonction \textbf{envie} est strictement négative. + + Un étudiant prépare un concours, pour lequel sa durée de travail varie entre 0 et 6 heures par jour. Il modélise sa satisfaction en fonction de son temps de travail quotidien par la fonction \textbf{satisfaction} $f$ dont la formule est donnée ci-dessous (x est exprimé en heures): + \[ f(x) = -\frac{194}{18} x^2 + \frac{197}{3}x \] + \begin{enumerate} + \item Quelle est la \textbf{satisfaction} de cet étudiant au bout de 1h, 4h et 6h de travail? + \item Déterminer combien de temps dure la période de \textbf{souhait}? + \item Cet étudiant arrivera-t-il à atteindre la saturation? + \item Combien de fois dans la journée, l'étudiant atteindra-t-il une satisfaction égale à 50? + \item Pensez-vous que cette fonction modélise correctement la \textbf{satisfaction} que peu avoir un étudiant au cours d'une journée de préparation? + \end{enumerate} +\end{exercise} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: + diff --git a/PreStSauveur/TESL/Convexite/fig/2018_Guyane_ex4.png b/PreStSauveur/TESL/Convexite/fig/2018_Guyane_ex4.png new file mode 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