| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2024 |
| Session | October |
| Marks | 4 |
| Topic | Curve Sketching |
| Type | Curve from derivative information |
| Difficulty | Moderate -0.8 This is a straightforward application of the relationship between a function and its derivative. Students need to recognize that turning points correspond to zeros of f'(x), and the sign of f'(x) determines whether the function is increasing/decreasing. The constraint of three stationary points (with only two being turning points) adds minimal complexity. This is easier than average as it requires only basic understanding of derivatives without calculation or novel insight. |
| Spec | 1.07c Sketch gradient function: for given curve |
\begin{enumerate}
\item The graph of $y = f ( x )$ (where $- 2 \leq x \leq 6$ ) has the following features:
\end{enumerate}
\begin{itemize}
\item A local maximum at $x = 0$.
\item A local minimum at $x = 2$.
\item No other turning points.
\item Three stationary points.
\end{itemize}
Sketch a possible graph of $y = f ^ { \prime } ( x )$ on the axes provided.\\
You can ignore the scale for the $y$-axis.\\
\includegraphics[max width=\textwidth, alt={}, center]{4c649001-3816-4cfa-9418-e3e427df1eb5-04_1269_1354_826_447}\\[0pt]
\\
\hfill \mbox{\textit{SPS SPS FM 2024 Q2 [4]}}