4MA0 Higher January 2018 Paper 4R Q16
16 \(y = 2x^3 - 9x^2 + 31\)
(a) Find \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\) (2)
Diagram NOT accurately drawn
The diagram shows a sketch of the curve with equation \(y = 2x^3 - 9x^2 + 31\)
The point \(M\) is a turning point on the curve.
(b) Work out the gradient of the line \(OM\).
Show clear algebraic working. (4)
Show clear algebraic working. (4)
| Scheme | Marks |
|---|---|
| M1 | |
| \(6x^2 - 18x\) | A1 |
| (2) |
Notes
M1: For \(6x^2\) or \(2 \times 3 \times x^2\) oe or \(-18x\) or \(-2 \times 9 \times x\) oe
| Scheme | Marks |
|---|---|
| \(6x^2 - 18x = 0\) | M1 |
| \(6x(x - 3) = 0\) \(x = 3\) (or \(x = 0\)) | A1 |
| (\(y\) =) \(2 \times 3^3 - 9 \times 3^2 + 31\) or 4 | M1 |
Gradient = \(\dfrac{4}{3}\) Answer: \(\dfrac{4}{3}\) oe | A1 |
| (4) | |
| (6 marks) |
Notes
M1: ft their part (a) = 0 if quadratic
A1: For \(x = 3\)
Dep on M1
M1: For substituting 3 in \(2x^3 - 9x^2 + 31\)