4400 Higher June 2009 Paper 4 Q17
17 A curve has equation \(y = x^2 + 3x\)
(a) Find \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\) (2)
(b) Find the gradient of the curve at the point where \(x = -4\) (1)
(c) The curve has a minimum point.
Find the coordinates of this minimum point. (3)
Find the coordinates of this minimum point. (3)
| Scheme | Marks |
|---|---|
| \(2x + 3\) | B2 |
| (2) |
Notes
B2: B1 each term (accept \(3x^0\))
| Scheme | Marks |
|---|---|
| “−5” | B1 |
| (1) |
Notes
B1: ft their \(ax + b\) \((a, b \ne 0)\)
| Scheme | Marks |
|---|---|
| “\(2x + 3\)” = 0 | M1 |
| \(x = -\frac{3}{2}\) | A1 |
| \(\left(-\frac{3}{2}, -\frac{9}{4}\right)\) oe | A1 |
| (3) | |
| (6 marks) |
Notes
M1: only ft their \(\frac{\mathrm{d}y}{\mathrm{d}x}\), if \(ax + b\) \((a, b \ne 0)\)
A1: cao dependent on \(2x + 3 = 0\)
A1: cao Answer dependent on \(2x + 3 = 0\) seen