| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2018 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Find stationary points |
| Difficulty | Standard +0.3 This is a straightforward implicit differentiation question requiring standard application of the product rule and chain rule, followed by solving a system of equations. While it involves multiple steps, the techniques are routine for C4 level with no novel insight required, making it slightly easier than average. |
| Spec | 1.07s Parametric and implicit differentiation |
\begin{enumerate}
\item The curve $C$ has equation
\end{enumerate}
$$x ^ { 2 } + x y + y ^ { 2 } - 4 x - 5 y + 1 = 0$$
(a) Use implicit differentiation to find $\frac { \mathrm { d } y } { \mathrm {~d} x }$ in terms of $x$ and $y$.\\
(b) Find the $x$ coordinates of the two points on $C$ where $\frac { \mathrm { d } y } { \mathrm {~d} x } = 0$
Give exact answers in their simplest form.\\
(Solutions based entirely on graphical or numerical methods are not acceptable.)\\
\hfill \mbox{\textit{Edexcel C4 2018 Q2 [10]}}