| Date | May 2008 | Marks available | 2 | Reference code | 08M.1.sl.TZ2.12 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Find | Question number | 12 | Adapted from | N/A |
Question
Consider the function \(f(x) = \frac{1}{2}{x^3} - 2{x^2} + 3\).
Find \(f'(x)\).
Find \(f''(x)\).
Find the equation of the tangent to the curve of \(f\) at the point \((1{\text{, }}1.5)\).
Markscheme
\(\frac{{3{x^2}}}{2} - 4x\) (A1)(A1) (C2)
Note: Award (A1) for each correct term and no extra terms; award (A1)(A0) for both terms correct and extra terms; (A0) otherwise.
[2 marks]
\(3x - 4\) (A1)(ft)(A1)(ft) (C2)
Note: accept \(3{x^1} - {4^0}\)
[2 marks]
\(y = - 2.5x + 4\) or equivalent (A1)(ft)(A1) (C2)
Note: Award (A1)(ft) on their (a) for \( - 2.5x\) (must have \(x\)), (A1) for \(4\) or equivalent correct answer only.
Accept \(y - 1.5 = - 2.5(x - 1)\)
[2 marks]
Examiners report
The final part of this question was not well answered. Most candidates could gain 4 marks in this question as most knew how to differentiate and they were required to do it twice. However, few realized that they could find the gradient of the tangent from their answer to part (a). This part was badly answered by most candidates.
The final part of this question was not well answered. Most candidates could gain 4 marks in this question as most knew how to differentiate and they were required to do it twice. However, few realized that they could find the gradient of the tangent from their answer to part (a). This part was badly answered by most candidates.
The final part of this question was not well answered. Most candidates could gain 4 marks in this question as most knew how to differentiate and they were required to do it twice. However, few realized that they could find the gradient of the tangent from their answer to part (a). This part was badly answered by most candidates.
