| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Stationary points and optimisation |
| Type | Classify nature of stationary points |
| Difficulty | Moderate -0.8 This is a standard textbook exercise on stationary points requiring routine differentiation, solving a quadratic equation, and applying the second derivative test. All steps are algorithmic with no problem-solving insight needed, making it easier than average but not trivial due to the multi-part structure and algebraic manipulation required. |
| Spec | 1.07d Second derivatives: d^2y/dx^2 notation1.07i Differentiate x^n: for rational n and sums1.07n Stationary points: find maxima, minima using derivatives1.07p Points of inflection: using second derivative |
The curve $C$ has equation
$y = 2x^3 - 5x^2 - 4x + 2$.
\begin{enumerate}[label=(\alph*)]
\item Find $\frac{dy}{dx}$.
[2]
\item Using the result from part (a), find the coordinates of the turning points of $C$.
[4]
\item Find $\frac{d^2y}{dx^2}$.
[2]
\item Hence, or otherwise, determine the nature of the turning points of $C$.
[2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q7 [10]}}