| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Find tangent at given point (polynomial/algebraic) |
| Difficulty | Moderate -0.8 This is a straightforward differentiation and tangent line question requiring only basic techniques: differentiate y = 2e^x + 3x^2 + 2 to get dy/dx = 2e^x + 6x, evaluate at x=0 to find gradient m=2, then use y-4=2(x-0). All steps are routine C3 procedures with no problem-solving or conceptual challenges beyond standard textbook exercises. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07j Differentiate exponentials: e^(kx) and a^(kx)1.07m Tangents and normals: gradient and equations |
The curve $C$ has equation $y = 2e^x + 3x^2 + 2$. The point $A$ with coordinates $(0, 4)$ lies on $C$. Find the equation of the tangent to $C$ at $A$. [5]
\hfill \mbox{\textit{Edexcel C3 Q1 [5]}}