| Exam Board | WJEC |
|---|---|
| Module | Unit 3 (Unit 3) |
| Year | 2024 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Stationary points and optimisation |
| Type | Find range where function increasing/decreasing |
| Difficulty | Standard +0.8 This question requires understanding the relationship between f'(x) and properties of f(x), specifically linking the sign of f'(x) to monotonicity and the gradient of f'(x) to concavity. While conceptually demanding (requiring second-derivative reasoning from a first-derivative graph), it's a standard A-level calculus application with clear visual cues. The multi-step reasoning and need to interpret graphical information about derivatives elevates it above average difficulty. |
| Spec | 1.07f Convexity/concavity: points of inflection1.07o Increasing/decreasing: functions using sign of dy/dx1.07p Points of inflection: using second derivative |
The diagram below shows a sketch of the graph of $y = f'(x)$ for the interval $[x_1, x_5]$.
\includegraphics{figure_13}
\begin{enumerate}[label=(\alph*)]
\item Find the interval on which $f(x)$ is both decreasing and convex. Give reasons for your answer. [2]
\item Write down the $x$-coordinate of a point of inflection of the graph of $y = f(x)$. [1]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 3 2024 Q13 [3]}}