| Date | November 2017 | Marks available | 3 | Reference code | 17N.1.sl.TZ0.14 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 14 | Adapted from | N/A |
Question
A function \(f\) is given by \(f(x) = 4{x^3} + \frac{3}{{{x^2}}} - 3,{\text{ }}x \ne 0\).
Write down the derivative of \(f\).
Find the point on the graph of \(f\) at which the gradient of the tangent is equal to 6.
Markscheme
\(12{x^2} - \frac{6}{{{x^3}}}\) or equivalent (A1)(A1)(A1) (C3)
Note: Award (A1) for \(12{x^2}\), (A1) for \( - 6\) and (A1) for \(\frac{1}{{{x^3}}}\) or \({x^{ - 3}}\). Award at most (A1)(A1)(A0) if additional terms seen.
[3 marks]
\(12{x^2} - \frac{6}{{{x^3}}} = 6\) (M1)
Note: Award (M1) for equating their derivative to 6.
\((1,{\text{ }}4)\)\(\,\,\,\)OR\(\,\,\,\)\(x = 1,{\text{ }}y = 4\) (A1)(ft)(A1)(ft) (C3)
Note: A frequent wrong answer seen in scripts is \((1,{\text{ }}6)\) for this answer with correct working award (M1)(A0)(A1) and if there is no working award (C1).
[3 marks]
