| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 7 |
| Topic | Stationary points and optimisation |
| Type | Classify nature of stationary points |
| Difficulty | Moderate -0.8 This is a straightforward calculus question requiring basic differentiation of polynomials, substitution to verify a stationary point, and using the second derivative test. All techniques are routine and mechanical with no problem-solving insight needed, making it easier than average but not trivial since it requires multiple steps and correct application of the second derivative test. |
| 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 |
A curve has equation $y = x^5 - 5x^4$.
\begin{enumerate}[label=(\alph*)]
\item Find $\frac{dy}{dx}$ and $\frac{d^2y}{dx^2}$. [3]
\item Verify that the curve has a stationary point when $x = 4$. [2]
\item Determine the nature of this stationary point. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 2017 Q2 [7]}}