| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Find stationary points |
| Difficulty | Moderate -0.3 Part (a) is a standard application of product rule and solving dy/dx=0, requiring ln x = -1 which gives x = 1/e. Part (b) is straightforward quotient rule differentiation showing the derivative is never zero. Both are routine C3 techniques with no problem-solving insight required, making this slightly easier than average. |
| Spec | 1.07n Stationary points: find maxima, minima using derivatives1.07q Product and quotient rules: differentiation |
\begin{enumerate}[label=(\alph*)]
\item Find the exact value of the $x$-coordinate of the stationary point of the curve $y = x \ln x$. [4]
\item The equation of a curve is $y = \frac{4x + c}{4x - c}$, where $c$ is a non-zero constant. Show by differentiation that this curve has no stationary points. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q6 [7]}}