| Date | May 2014 | Marks available | 2 | Reference code | 14M.1.sl.TZ2.15 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Find | Question number | 15 | Adapted from | N/A |
Question
A function is given as \(f(x) = 2{x^3} - 5x + \frac{4}{x} + 3,{\text{ }} - 5 \leqslant x \leqslant 10,{\text{ }}x \ne 0\).
Write down the derivative of the function.
Use your graphic display calculator to find the coordinates of the local minimum point of \(f(x)\) in the given domain.
Markscheme
\(6{x^2} - 5 - \frac{4}{{{x^2}}}\) (A1)(A1)(A1)(A1) (C4)
Note: Award (A1) for \(6{x^2}\), (A1) for \(–5\), (A1) for \(–4\), (A1) for \({x^{ - 2}}\) or \(\frac{1}{{{x^2}}}\).
Award at most (A1)(A1)(A1)(A0) if additional terms are seen.
[4 marks]
\((1.15,{\text{ }} 3.77)\) \(\left( {{\text{(1.15469..., 3.76980...)}}} \right)\) (A1)(A1) (C2)
Notes: Award (A1)(A1) for “\(x = 1.15\) and \(y = 3.77\)”.
Award at most (A0)(A1)(ft) if parentheses are omitted.
[2 marks]
