We consider a function $f$ defined on $[0; +\infty[$, represented by the curve $\mathscr{C}$ below. The line $T$ is tangent to the curve $\mathscr{C}$ at point A with abscissa $\frac{5}{2}$.
Draw up, by graphical reading, the table of variations of the function $f$ on the interval $[0;5]$.
What does the curve $\mathscr{C}$ appear to present at point A?
The derivative $f'$ and the second derivative $f''$ of the function $f$ are represented by the curves $\mathscr{C}_1$ and $\mathscr{C}_2$. Associate with each of these two functions the curve that represents it. This choice will be justified.
Can the curve $\mathscr{C}_3$ be the graphical representation on $[0; +\infty[$ of a primitive of the function $f$? Justify.
We consider a function $f$ defined on $[0; +\infty[$, represented by the curve $\mathscr{C}$ below. The line $T$ is tangent to the curve $\mathscr{C}$ at point A with abscissa $\frac{5}{2}$.
\begin{enumerate}
\item Draw up, by graphical reading, the table of variations of the function $f$ on the interval $[0;5]$.
\item What does the curve $\mathscr{C}$ appear to present at point A?
\item The derivative $f'$ and the second derivative $f''$ of the function $f$ are represented by the curves $\mathscr{C}_1$ and $\mathscr{C}_2$. Associate with each of these two functions the curve that represents it. This choice will be justified.
\item Can the curve $\mathscr{C}_3$ be the graphical representation on $[0; +\infty[$ of a primitive of the function $f$? Justify.
\end{enumerate}