| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Stationary points and optimisation |
| Type | Prove or show increasing/decreasing function |
| Difficulty | Moderate -0.8 This is a straightforward application of differentiation to show a function is decreasing. Students need only find f'(x) = -1 - 3x², recognize it's always negative (sum of negative constants), and conclude the function is decreasing everywhere. It's simpler than average A-level questions as it requires just one derivative and basic inequality reasoning with no problem-solving insight. |
| Spec | 1.07o Increasing/decreasing: functions using sign of dy/dx |
2.
$$f ( x ) = 2 - x - x ^ { 3 } .$$
Show that $\mathrm { f } ( x )$ is decreasing for all values of $x$.\\
\hfill \mbox{\textit{OCR C1 Q2 [4]}}