| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Determine nature of stationary points |
| Difficulty | Moderate -0.8 This is a straightforward application of basic differentiation rules (power rule) and standard stationary point analysis. All parts are routine: differentiate twice, substitute x=4 to verify dy/dx=0, then use the second derivative test. No problem-solving insight required, just mechanical application of standard techniques. |
| 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 derivatives1.07o Increasing/decreasing: functions using sign of dy/dx |
2 A curve has equation $y = x ^ { 5 } - 5 x ^ { 4 }$.
\begin{enumerate}[label=(\alph*)]
\item Find $\frac { \mathrm { d } y } { \mathrm {~d} x }$ and $\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }$.
\item Verify that the curve has a stationary point when $x = 4$.
\item Determine the nature of this stationary point.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 Q2 [7]}}