| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2008 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Differentiating Transcendental Functions |
| Type | Show stationary point exists or gradient has specific property |
| Difficulty | Moderate -0.3 This is a straightforward differentiation question requiring the product rule on x²ln(x), setting dy/dx = 0, and solving a simple equation. It's slightly easier than average because the question tells you exactly what to show (no problem-solving required) and the algebra is minimal—just factorize x(2ln(x) + 1) = 0 and solve ln(x) = -1/2. |
| Spec | 1.07l Derivative of ln(x): and related functions1.07n Stationary points: find maxima, minima using derivatives1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates |
5 Show that the curve $y = x ^ { 2 } \ln x$ has a stationary point when $x = \frac { 1 } { \sqrt { \mathrm { e } } }$.
\hfill \mbox{\textit{OCR MEI C3 2008 Q5 [6]}}