June 2018 Paper 2 Q9
9 \(y = \dfrac{2x^7 + 15x^2}{3x}\)
Work out the value of \(x\) when \(\quad \dfrac{\mathrm{d}y}{\mathrm{d}x} = 133\) [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{2x^6}{3}\) or \(\dfrac{2}{3}x^6\) or \(\dfrac{15x}{3}\) or \(5x\) | M1 | implied by \(\dfrac{2x^6 + \mathrm{a}}{3}\) or \(\dfrac{\mathrm{b} + 15x}{3}\) a can be numerical or algebraic b can be numerical or algebraic allow 0.66… or 0.67 for \(\dfrac{2}{3}\) |
| \(6 \times \dfrac{2x^5}{3}\) or \(\dfrac{12x^5}{3}\) or \(4x^5\) or \(\dfrac{15}{3}\) or 5 | M1dep | correct differentiation of one correct term implied by \(\dfrac{6 \times 2x^5 + \mathrm{a}}{3}\) or \(\dfrac{\mathrm{b} + 15}{3}\) |
| \(4x^5 + 5 = 133\) or \(4x^5 = 128\) or \(x^5 = 32\) or \(\sqrt[5]{32}\) | A1 | oe both correct terms differentiated and simplified correctly and equated to 133 |
| 2 | A1 |
Additional guidance
| \(\dfrac{14x^6 + 30x}{3}\) | Zero |