June 2023 Paper 3 Q5
5 A curve has equation \(y = 3\mathrm{e}^{2x}\)
Find the gradient of the curve at the point where \(y = 10\) [3 marks]
| Scheme | Marks | AO |
|---|---|---|
| Obtains \(2 \times 3\mathrm{e}^{2x}\) or \(6\mathrm{e}^{2x}\) or \(2y\) PI by correct answer | B1 | 1.1b |
| Substitutes \(y = 10\) or \(3\mathrm{e}^{2x} = 10\) in their \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\) or substitutes \(x\) = [0.6, 0.602] or \(x = \dfrac{1}{2}\ln\left(\dfrac{10}{3}\right)\) OE in their \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\) | M1 | 1.1a |
| Obtains 20 CAO 20 cannot come from a rounded value for 20 seen | A1 | 1.1b |
| (3 marks) |