| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2008 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Find stationary points |
| Difficulty | Standard +0.3 This is a straightforward implicit differentiation question with standard follow-through steps. Part (i) requires applying the product rule twice and rearranging—routine C4 technique. Parts (ii)(a) and (ii)(b) involve simple algebraic manipulation (setting numerator to zero, substituting into original equation). No novel insight required, just methodical application of learned procedures, making it slightly easier than average. |
| Spec | 1.07n Stationary points: find maxima, minima using derivatives1.07s Parametric and implicit differentiation |
3 The equation of a curve is $x ^ { 2 } y - x y ^ { 2 } = 2$.
\begin{enumerate}[label=(\roman*)]
\item Show that $\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { y ^ { 2 } - 2 x y } { x ^ { 2 } - 2 x y }$.
\item (a) Show that, if $\frac { \mathrm { d } y } { \mathrm {~d} x } = 0$, then $y = 2 x$.\\
(b) Hence find the coordinates of the point on the curve where the tangent is parallel to the $x$-axis.
\end{enumerate}
\hfill \mbox{\textit{OCR C4 2008 Q3 [8]}}