| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2009 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Stationary points and optimisation |
| Type | Find range where function increasing/decreasing |
| Difficulty | Moderate -0.8 This is a straightforward application of standard differentiation techniques: find dy/dx, set equal to zero, solve the quadratic, then use the second derivative or sign test to determine where the function is increasing. It requires only routine procedures with no problem-solving insight, making it easier than average but not trivial since it involves solving a quadratic and interpreting the results for increasing intervals. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07n Stationary points: find maxima, minima using derivatives1.07o Increasing/decreasing: functions using sign of dy/dx |
6 Use calculus to find the $x$-coordinates of the turning points of the curve $y = x ^ { 3 } - 6 x ^ { 2 } - 15 x$. Hence find the set of values of $x$ for which $x ^ { 3 } - 6 x ^ { 2 } - 15 x$ is an increasing function.
\hfill \mbox{\textit{OCR MEI C2 2009 Q6 [5]}}