| Exam Board | Edexcel |
|---|---|
| Module | P2 (Pure Mathematics 2) |
| Year | 2020 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Stationary points and optimisation |
| Type | Determine constant from stationary point condition |
| Difficulty | Standard +0.3 This is a straightforward multi-part differentiation question requiring standard techniques: finding k using the stationary point condition, using the second derivative test to determine nature, and solving a cubic equation. All steps are routine for P2 level with no novel insight required, making it slightly easier than average. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07n Stationary points: find maxima, minima using derivatives1.07o Increasing/decreasing: functions using sign of dy/dx1.07p Points of inflection: using second derivative |
10. A curve $C$ has equation
$$y = 4 x ^ { 3 } - 9 x + \frac { k } { x } \quad x > 0$$
where $k$ is a constant.\\
The point $P$ with $x$ coordinate $\frac { 1 } { 2 }$ lies on $C$.\\
Given that $P$ is a stationary point of $C$,
\begin{enumerate}[label=(\alph*)]
\item show that $k = - \frac { 3 } { 2 }$
\item Determine the nature of the stationary point at $P$, justifying your answer.
The curve $C$ has a second stationary point.
\item Using algebra, find the $x$ coordinate of this second stationary point.\\
\includegraphics[max width=\textwidth, alt={}, center]{08aac50c-7317-4510-927a-7f5f2e00f485-26_2255_50_312_1980}
\end{enumerate}
\hfill \mbox{\textit{Edexcel P2 2020 Q10 [10]}}