| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Stationary points and optimisation |
| Type | Second derivative test justification |
| Difficulty | Moderate -0.8 This is a straightforward C1 stationary points question requiring routine differentiation of a polynomial, setting the derivative to zero, and using the second derivative test. All steps are standard textbook procedures with no problem-solving insight needed, making it easier than average but not trivial since it requires multiple connected steps. |
| 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 |
7.
$$f ( x ) = x ^ { 3 } - 9 x ^ { 2 }$$
(i) Find $\mathrm { f } ^ { \prime } ( x )$.\\
(ii) Find $\mathrm { f } ^ { \prime \prime } ( x )$.\\
(iii) Find the coordinates of the stationary points of the curve $y = \mathrm { f } ( x )$.\\
(iv) Determine whether each stationary point is a maximum or a minimum point.\\
\hfill \mbox{\textit{OCR C1 Q7 [9]}}