| Exam Board | CAIE |
|---|
| Module | FP1 (Further Pure Mathematics 1) |
|---|
| Year | 2013 |
|---|
| Session | June |
|---|
| Topic | Implicit equations and differentiation |
|---|
4 Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = - \frac { 4 } { 3 }\) at the point \(A ( 1 , - 2 )\) on the curve with equation
$$y ^ { 3 } - 3 x ^ { 2 } y + 2 = 0$$
and find the value of \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) at \(A\).