Specimen 2020 Paper 1 Q19
19
\[\mathrm{f}(x) = 2x^3 - 12x^2 + 25x - 11\]Use differentiation to show that \(\mathrm{f}(x)\) is an increasing function for all values of \(x\). [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(6x^2 - 24x + 25\) | M1 | allow one error |
| \(6(x^2 - 4x) \ldots\) | M1dep | ft their \(6x^2 - 24x + 25\) must have 3 term quadratic |
| \(6(x - 2)^2 \ldots\) | M1dep | ft their \(6(x^2 - 4x) \ldots\) |
| \(6(x - 2)^2 + 1\) and valid argument that this is \(\gt 0\) | A1 |