| Exam Board | CAIE |
|---|
| Module | FP1 (Further Pure Mathematics 1) |
|---|
| Year | 2012 |
|---|
| Session | June |
|---|
| Topic | Implicit equations and differentiation |
|---|
3 The curve \(C\) has equation
$$x y + ( x + y ) ^ { 3 } = 1$$
Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = - \frac { 3 } { 4 }\) at the point \(A ( 1,0 )\) on \(C\).
Find the value of \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) at \(A\).