| Exam Board | CAIE |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2011 |
| Session | November |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
5 The point $P ( 2,1 )$ lies on the curve with equation
$$x ^ { 3 } - 2 y ^ { 3 } = 3 x y$$
Find\\
(i) the value of $\frac { \mathrm { d } y } { \mathrm {~d} x }$ at $P$,\\
(ii) the value of $\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }$ at $P$.
\hfill \mbox{\textit{CAIE FP1 2011 Q5}}