| Date | May 2008 | Marks available | 2 | Reference code | 08M.1.sl.TZ1.3 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 3 | Adapted from | N/A |
Question
Consider the function \(f(x) = 2{x^3} - 5{x^2} + 3x + 1\).
Find \(f'(x)\).
Write down the value of \(f'(2)\).
Find the equation of the tangent to the curve of \(y = f(x)\) at the point \((2{\text{, }}3)\).
Markscheme
\(f'(x) = 6{x^2} - 10x + 3\) (A1)(A1)(A1) (C3)
Notes: Award (A1) for each correct term and no extra terms.
Award (A1)(A1)(A0) if each term correct and extra term seen.
Award(A1)(A0)(A0) if two terms correct and extra term seen.
Award (A0) otherwise.
[3 marks]
\(f'(2) = 7\) (A1)(ft) (C1)
[1 mark]
\(y = 7x - 11\) or equivalent (A1)(ft)(A1)(ft) (C2)
Note: Award (A1)(ft) on their (b) for \(7x\) (must have \(x\)), (A1)(ft) for \( - 11\). Accept \(y - 3 = 7(x - 2)\) .
[2 marks]
Examiners report
Most candidates were able to score full marks for parts (a) and (b). When mistakes were made in part (a) follow-through marks could be awarded for part (b) provided working was shown. Part (c) was disappointing with many candidates not realizing that the answer in (b) was the gradient of the tangent line.
Most candidates were able to score full marks for parts (a) and (b). When mistakes were made in part (a) follow-through marks could be awarded for part (b) provided working was shown. Part (c) was disappointing with many candidates not realizing that the answer in (b) was the gradient of the tangent line.
Most candidates were able to score full marks for parts (a) and (b). When mistakes were made in part (a) follow-through marks could be awarded for part (b) provided working was shown. Part (c) was disappointing with many candidates not realizing that the answer in (b) was the gradient of the tangent line.
