| Exam Board | WJEC |
|---|---|
| Module | Unit 3 (Unit 3) |
| Year | 2023 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Stationary points and optimisation |
| Type | Classify nature of stationary points |
| Difficulty | Standard +0.3 This is a straightforward calculus question requiring finding f''(x), solving f''(x)=0 for the inflection point, checking f'(x) at that point to determine if stationary, and using f''(x)<0 for concavity. All steps are routine differentiation and algebraic manipulation with no conceptual challenges, making it slightly easier than average. |
| Spec | 1.07e Second derivative: as rate of change of gradient1.07f Convexity/concavity: points of inflection1.07p Points of inflection: using second derivative |
A curve C has equation $f(x) = 5x^3 + 2x^2 - 3x$.
\begin{enumerate}[label=(\alph*)]
\item Find the $x$-coordinate of the point of inflection. State, with a reason, whether the point of inflection is stationary or non-stationary. [5]
\item Determine the range of values of $x$ for which C is concave. [2]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 3 2023 Q11 [7]}}