4MA0 Higher June 2015 Paper 4 Q21
21 \(y = x^3 + 6x^2 + 5\)
(a) Find \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\) (2)
The curve with equation \(y = x^3 + 6x^2 + 5\) has two turning points.
(b) Work out the coordinates of these two turning points.
Show your working clearly. (4)
Show your working clearly. (4)
| Scheme | Marks |
|---|---|
| \(3x^2 + 12x\) | B2 |
| (2) |
Notes
B2: B1 for \(3x^2\) or \(12x\)
| Scheme | Marks |
|---|---|
| " \(3x^2 + 12x\) " = 0 | M1 |
| \(3x(x + 4) = 0\) or \(x(x + 4) = 0\) or \(x(3x + 12) = 0\) or correct use of the formula (all values correctly substituted) or completing the square (as far as \((3)((x + 2)^2 - 4) = 0\)) | M1 |
| \(x = 0\) and \(x = -4\) | A1 |
| (0, 5) and (−4, 37) | A1 |
| (4) |
Notes
M1: ft
M1: ft as long as in the form of a quadratic equation.
A1: dep on M1
A1: Could be \(x = 0, y = 5; x = -4, y = 37\)