4MA0 Higher January 2017 Paper 3R Q20
20 A curve has equation \(\;y = x^3 - 4x^2 + 5x + 4\)
(a) Find \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\) (2)
(b) Find the \(x\) coordinates of the points where the curve with equation \(\;y = x^3 - 4x^2 + 5x + 4\;\) has a gradient of 1
Show clear algebraic working. (4)
Show clear algebraic working. (4)
| Scheme | Marks |
|---|---|
| M1 | |
| \(3x^2 - 8x + 5\) | A1 |
| (2) |
Notes
M1: for any 2 of \(3x^2\) or \(-8x\) or \(+5\) differentiated correctly
| Scheme | Marks |
|---|---|
| \(3x^2 - 8x + 5 = 1\) | M1 |
| \(3x^2 - 8x + 4 = 0\) | M1 |
| eg \((3x - 2)(x - 2) = 0\) | M1 |
| \(\dfrac{2}{3}\) , 2 | A1 |
| (4) | |
| (6 marks) |
Notes
M1: ft from (a)
M1: ft rearrange ready to solve, ft as long as \(ax^2 - bx + c\)
M1: ft correct method to solve quadratic – if using formula, every term to be substituted correctly as long as \(ax^2 - bx + c\)
A1: cao dep on M2
Ignore any attempts to find y values