4MA0 Higher June 2016 Paper 3R Q15
15 \(y = x^3 - \dfrac{9}{2}x^2 - 54x + 10\)
(a) Find \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\) (2)
The curve with equation \(y = x^3 - \dfrac{9}{2}x^2 - 54x + 10\) has two turning points.
(b) Find the \(x\) coordinate of each of these two points. (3)
| Scheme | Marks |
|---|---|
| M1 | |
| \(3x^2 - 9x - 54\) | A1 |
| (2) |
Notes
M1: For any two of \(3x^2\), \(-2 \times \dfrac{9}{2}x\), or \(-54\)
| Scheme | Marks |
|---|---|
| \(3x^2 - 9x - 54 = 0\) | M1ft |
Eg \(3(x - 6)(x + 3)\) ( = 0 ) or (\(x\) =) \(\dfrac{-(-9) \pm \sqrt{(-9)^2 - 4 \times 3 \times -54}}{2 \times 3}\) | M1ft |
| \(x = -3\) and \(x = 6\) | A1 |
| (3) |
Notes
M1ft: For letting (a) = 0
M1ft: For correct factors or correct substitution into the quadratic formula
Only ft for a 3 term quadratic & if M1 scored in (a)