| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Stationary points and optimisation |
| Type | Find stationary points coordinates |
| Difficulty | Moderate -0.8 This is a straightforward application of basic differentiation and finding stationary points. It requires only polynomial differentiation (power rule), setting the derivative to zero, and solving a simple quadratic. This is a standard textbook exercise with no problem-solving insight required, making it easier than average. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07n Stationary points: find maxima, minima using derivatives |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(\frac{dy}{dx} = 3x^2 - 12\) | M1, A1 | Total: 2 marks |
| (ii) \(3x^2 - 12 = 0\) when \(x = \pm 2\) \(\Rightarrow (2, -16)\) and \((-2, 16)\) | M1, B1, B1 | Total: 3 marks |
**(i)** $\frac{dy}{dx} = 3x^2 - 12$ | M1, A1 | **Total: 2 marks**
**(ii)** $3x^2 - 12 = 0$ when $x = \pm 2$ $\Rightarrow (2, -16)$ and $(-2, 16)$ | M1, B1, B1 | **Total: 3 marks**4 You are given that $y = x ^ { 3 } - 12 x$.\\
(i) Find $\frac { \mathrm { d } y } { \mathrm {~d} x }$.\\
(ii) Hence find the coordinates of the turning points of the curve.
\hfill \mbox{\textit{OCR MEI C2 Q4 [5]}}