4400 Higher November 2008 Paper 4 Q20
20
(a) Differentiate with respect to \(x\)
(i) \(3x^2 - x\)
(ii) \(\dfrac{1}{x}\)
(4)(b) Find the coordinates of the points on the curve \(y = x^3\) where the gradient is 12 (3)
| Scheme | Marks |
|---|---|
| (i) Answer: \(6x - 1\) | B2 |
| (ii) Answer: \(-x^{-2}\) or \(-1x^{-2}\) or \(-\frac{1}{x^2}\) | B2 |
| (4) |
Notes
B2: B1 for \(6x\) or \(6x^1\) B1 for \(-1\)
B2: B1 for \(x^{-2}\) oe
−B1 for incorrect re-writing eg \(-\frac{1}{x^{-2}}\)
| Scheme | Marks |
|---|---|
| \(3x^2\) | B1 |
| “\(3x^2\)” = 12 | M1 |
| (−2, −8) (2, 8) | A1 |
| (3) | |
| (7 marks) |