| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2013 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Stationary points and optimisation |
| Type | Second derivative test justification |
| Difficulty | Moderate -0.3 This is a straightforward C2 differentiation question requiring standard techniques: differentiate (including x^{1/2} term), set derivative to zero, solve for x, substitute back, and use second derivative test. While it involves multiple steps and careful algebraic manipulation of surds, it follows a completely routine procedure with no problem-solving 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 derivatives1.07p Points of inflection: using second derivative |
\begin{enumerate}
\item The curve with equation
\end{enumerate}
$$y = x ^ { 2 } - 32 \sqrt { } ( x ) + 20 , \quad x > 0$$
has a stationary point $P$.
Use calculus\\
(a) to find the coordinates of $P$,\\
(b) to determine the nature of the stationary point $P$.\\
\hfill \mbox{\textit{Edexcel C2 2013 Q9 [9]}}