| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Find normal equation at point |
| Difficulty | Standard +0.3 This is a standard implicit differentiation question requiring students to differentiate both sides with respect to x, apply the product rule to the -2xy term, solve for dy/dx, substitute the given point to find the gradient, then find the normal (negative reciprocal) and write the equation. While it involves multiple steps and careful algebraic manipulation, it follows a completely routine procedure taught explicitly in C4 with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.07m Tangents and normals: gradient and equations1.07s Parametric and implicit differentiation |
A curve has equation
$$x^3 - 2xy - 4x + y^3 - 51 = 0.$$
Find an equation of the normal to the curve at the point $(4, 3)$, giving your answer in the form $ax + by + c = 0$, where $a$, $b$ and $c$ are integers.
[8]
\hfill \mbox{\textit{Edexcel C4 Q2 [8]}}