| Date | May 2008 | Marks available | 2 | Reference code | 08M.2.sl.TZ1.5 |
| Level | SL only | Paper | 2 | Time zone | TZ1 |
| Command term | Complete | Question number | 5 | Adapted from | N/A |
Question
The diagram below shows part of the graph of the gradient function, \(y = f'(x)\) .
On the grid below, sketch a graph of \(y = f''(x)\) , clearly indicating the x-intercept.
Complete the table, for the graph of \(y = f(x)\) .
Justify your answer to part (b) (ii).
Markscheme
A1A1 N2
Note: Award A1 for negative gradient throughout, A1 for x-intercept of q. It need not be linear.
[2 marks]
A1A1 N1N1
METHOD 1
Second derivative is zero, second derivative changes sign. R1R1 N2
METHOD 2
There is a maximum on the graph of the first derivative. R2 N2
Examiners report
Several candidates had a correct sketch in part (a).
The majority of the errors occurred in parts (b) and (c). In part (b), some seemed to just guess while others left it blank.
In part (c), justification lacked completeness. For example, many stated that the second derivative must equal zero but said nothing of its change in sign.
