June 2023 Paper 2 Q5
5 \(\quad y = 0.5x^4\)
Work out the value of \(x\) for which the rate of change of \(y\) with respect to \(x\) is 6.75 [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(2x^3\) | M1 | oe eg \(4 \times 0.5x^{4 - 1}\) |
| \(x^3 = \dfrac{6.75}{2}\) or \(x^3 = 3.375\) or \(\sqrt[3]{3.375}\) | M1dep | oe eg \(\dfrac{27}{8} = x^3\) or \(\sqrt[3]{\dfrac{27}{8}}\) |
| 1.5 or \(\dfrac{3}{2}\) | A1 | oe value eg \(1\dfrac{1}{2}\) |
Additional guidance
| Up to M1 may be awarded for correct work with no answer or incorrect answer, even if this is seen amongst multiple attempts | |
| Condone incorrect notation eg \(y = 2x^3\) | 1st M1 |
| Ignore higher derivatives | |
| Ignore attempt at \(y\)-coordinate | |
| \(2x^3 = 6.75\) or \(8x^3 = 27\) with no further correct work | M1M0 |