October 2020 Paper 2 Q3
3 You are given that \(y = 4x + \sin 8x\).
(a) Find \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\). [2]
(b) Find the smallest positive value of \(x\) for which \(\dfrac{\mathrm{d}y}{\mathrm{d}x} = 0\), giving your answer in an exact form. [2]
| Scheme | Marks | AO |
|---|---|---|
| \(4 + 8\cos 8x\) | M1* A1 | 1.1 1.1 |
| [2] |
Notes
M1*: differentiation with either term correct
A1: all correct
| Scheme | Marks | AO |
|---|---|---|
| attempt to solve their \(4 + 8\cos 8x = 0\) | M1dep* | 1.1 |
| \(\frac{\pi}{12}\) isw cao | A1 | 1.1 |
| [2] |
Notes
M1dep*: one intermediate step seen