4400 Higher November 2010 Paper 3 Q16
16 A curve has equation \(y = x^3 + 3x^2 - 24x\)
(a) Find \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\) (3)
(b) Find the coordinates of the turning points of the curve. (5)
| Scheme | Marks |
|---|---|
| \(3x^2 + 6x - 24\) | B3 |
| (3) |
Notes
B3: B1 each term
| Scheme | Marks |
|---|---|
| “\(3x^2 + 6x - 24\)” = 0 | M1ft |
| \((3x + 12)(x - 2)\) oe | M1ft |
| \(x = -4\) or 2 | A1 |
| sub both \(x\) values | M1ft |
| (−4, 80), (2, −28) | A1 |
| (5) | |
| (8 marks) |
Notes
M1ft: Must be a 3 term quadratic
M1ft: or “\(\dfrac{-6 \pm \sqrt{6^2 - 4 \times 3 \times -24}}{2 \times 3}\)” condone 1 sign error
A1: cao
A1: cao (needs first 2 M’s)