| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Stationary points and optimisation |
| Type | Determine constant from stationary point condition |
| Difficulty | Standard +0.3 This is a straightforward stationary points question requiring differentiation, substituting x=-2 into dy/dx=0 to find k, then finding the second derivative to identify the inflection point. All steps are standard A-level techniques with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07n Stationary points: find maxima, minima using derivatives1.07p Points of inflection: using second derivative |
6 A curve has equation $y = x ^ { 2 } + k x - 4 x ^ { - 1 }$ 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.
\end{itemize}
\hfill \mbox{\textit{OCR H240/03 Q6 [7]}}