| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 7 |
| Topic | Stationary points and optimisation |
| Type | Determine constant from stationary point condition |
| Difficulty | Standard +0.3 This is a straightforward calculus optimization problem requiring differentiation to find k from the minimum condition, then second derivative analysis for the inflection point. The steps are standard A-level techniques with no novel insight required, though the multi-part nature and inflection point verification make it slightly above routine drill exercises. |
| Spec | 1.07n Stationary points: find maxima, minima using derivatives1.07p Points of inflection: using second derivative |
A curve has equation $y = x^2 + kx - 4x^{-1}$ where $k$ is a constant.
Given that the curve has a minimum point when $x = -2$
\begin{itemize}
\item find the value of $k$
\item show that the curve has a point of inflection which is not a stationary point. [7]
\end{itemize}
\hfill \mbox{\textit{OCR H240/03 2017 Q6 [7]}}