| Exam Board | CAIE |
|---|
| Module | FP1 (Further Pure Mathematics 1) |
|---|
| Year | 2011 |
|---|
| Session | June |
|---|
| Topic | Implicit equations and differentiation |
|---|
4 The curve \(C\) has equation
$$2 x y ^ { 2 } + 3 x ^ { 2 } y = 1$$
Show that, at the point \(A ( - 1,1 )\) on \(C , \frac { \mathrm {~d} y } { \mathrm {~d} x } = - 4\).
Find the value of \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) at \(A\).