4400 Higher November 2007 Paper 4 Q20
20 A curve has equation \(y = x^3 - 5x^2 + 8x - 7\)
(a) Find the gradient of the curve at \((2, -3)\). (4)
(b) What does your answer to part (a) tell you about the point \((2, -3)\)? (1)
| Scheme | Marks |
|---|---|
| \(\dfrac{\mathrm{d}y}{\mathrm{d}x} = 3x^2 - 10x + 8\) | B2 |
| \(3 \times 2^2 - 10 \times 2 + 8\) | M1 |
| 0 | A1 |
| (4) |
Notes
B2: B1 for 2 correct terms
M1: (dep on at least B1) for substituting \(x = 2\)
A1: cao
| Scheme | Marks |
|---|---|
| (could be) turning point, max or min, (is) stationary point tangent is parallel to the \(x\)-axis | B1 |
| (1) | |
| (5 marks) |