| 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 range where function increasing/decreasing |
| Difficulty | Moderate -0.3 This is a straightforward application of differentiation to find increasing intervals: differentiate to get 3x² - 6, set > 0, and solve the quadratic inequality. Slightly easier than average as it requires only basic differentiation and solving a simple inequality, though students must remember the connection between f'(x) > 0 and increasing functions. |
| Spec | 1.07o Increasing/decreasing: functions using sign of dy/dx |
Question 2:
B1: $2 \mid 3x^2 - 6$ seen
M1: their $y' = 0$ or $y' > 0$ or $y' \geq 0$; must be quadratic with at least one of only two terms correct
A1: $2$ and $-2$ identified; may be implied by use with inequalities or by $\pm 1.41[4213562]$ to 3 sf or more
A1: $x < -2$ or $x \leq -2$ isw
A1: $x > 2$ or $x \geq 2$; if A1A0A0, allow SC1 for fully correct answer in decimal form to 3 sf or more or A2 for $x > 2$ or $x \geq 2$; $x = 2$ implies A1
NB: just $-2 > x > 2$ or $2 < x < -2$ or $x > \pm 2$ implies the first A1 then A0A0
[5]2 Use calculus to find the set of values of $x$ for which $x ^ { 3 } - 6 x$ is an increasing function.
\hfill \mbox{\textit{OCR MEI C2 Q2 [5]}}