| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| 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. Students differentiate the cubic, set f'(x) > 0, solve the resulting quadratic inequality using standard methods (factorising or quadratic formula). It's slightly easier than average because it's a routine procedure with no conceptual surprises, though solving the inequality requires care with signs. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable1.07i Differentiate x^n: for rational n and sums1.07o Increasing/decreasing: functions using sign of dy/dx |
3.
$$f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - 3 x + 7$$
Find the set of values of $x$ for which $\mathrm { f } ( x )$ is increasing.\\
\hfill \mbox{\textit{OCR C1 Q3 [5]}}