4400 Higher June 2007 Paper 3 Q17
17 A curve has equation \(y = x^2 + \dfrac{16}{x}\)
The curve has one turning point.
Find \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\) and use your answer to find the coordinates of this turning point.
(4)
| Scheme | Marks |
|---|---|
| \(\left(\dfrac{\mathrm{d}y}{\mathrm{d}x} =\right) 2x - \dfrac{16}{x^2}\) | B1 |
| B1 | |
| \(\text{“}2x \pm \dfrac{16}{x^2}\text{”} = 0\) | M1 |
| (2, 12) | A1 |
| (4) | |
| (4 marks) |
Notes
B1: for \(2x\)
B1: for \(\pm\dfrac{16}{x^2}\) or \(\pm 16x^{-2}\)
A1: cao For answer (2, 12) with no preceding marks scored, award B0 B0 M1 A1