| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2014 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Find second derivative |
| Difficulty | Moderate -0.3 This is a straightforward C2 differentiation question requiring standard techniques: differentiating x and x^(-2), finding stationary points by setting dy/dx=0, using the second derivative test, and finding a normal line equation. All steps are routine applications of core methods with no problem-solving insight required, making it slightly easier than average but not trivial due to the algebraic manipulation and multiple parts. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07m Tangents and normals: gradient and equations1.07n Stationary points: find maxima, minima using derivatives1.07o Increasing/decreasing: functions using sign of dy/dx |
\includegraphics{figure_11}
Fig. 11 shows a sketch of the curve with equation $y = x - \frac{4}{x^2}$.
\begin{enumerate}[label=(\roman*)]
\item Find $\frac{dy}{dx}$ and show that $\frac{d^2y}{dx^2} = -\frac{24}{x^4}$. [3]
\item Hence find the coordinates of the stationary point on the curve. Verify that the stationary point is a maximum. [5]
\item Find the equation of the normal to the curve when $x = -1$. Give your answer in the form $ax + by + c = 0$. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C2 2014 Q11 [13]}}