| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chain Rule |
| Type | Find stationary points and nature |
| Difficulty | Standard +0.8 This question requires applying the quotient rule to a function involving logarithms, then solving the resulting equation dy/dx = 0 to find stationary points. While the quotient rule application is standard C3 content, solving the resulting equation requires careful algebraic manipulation and recognizing that the numerator must equal zero, leading to a transcendental equation that simplifies nicely. The multi-step nature and need to work with ln x algebraically makes this moderately harder than average. |
| Spec | 1.07n Stationary points: find maxima, minima using derivatives1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates |
A curve has equation $y = \frac{x}{2 + 3\ln x}$. Find $\frac{dy}{dx}$. Hence find the exact coordinates of the stationary point of the curve.
\hfill \mbox{\textit{OCR MEI C3 Q6}}