The curve $\mathscr{C}$ below represents a function $f$ defined and twice differentiable on $]0; +\infty[$. We know that:
\begin{itemize}
  \item the maximum of the function $f$ is reached at the point with abscissa 3;
  \item the point P with abscissa 5 is the unique inflection point of the curve $\mathscr{C}$.
\end{itemize}
We have:\\
A. for all $x \in ]0; 5[$, $f(x)$ and $f'(x)$ have the same sign;\\
C. for all $x \in ]0; 5[$, $f'(x)$ and $f''(x)$ have the same sign;\\
B. for all $x \in ]5; +\infty[$, $f(x)$ and $f'(x)$ have the same sign;\\
D. for all $x \in ]5; +\infty[$, $f(x)$ and $f''(x)$ have the same sign.