Date | May 2013 | Marks available | 2 | Reference code | 13M.1.sl.TZ1.15 |
Level | SL only | Paper | 1 | Time zone | TZ1 |
Command term | Find | Question number | 15 | Adapted from | N/A |
Question
Consider the function f(x)=ax3−3x+5, where a≠0.
Find f′(x).
Write down the value of f′(0).
The function has a local maximum at x = −2.
Calculate the value of a.
Markscheme
f′(x)=3ax2−3 (A1)(A1) (C2)
Note: Award a maximum of (A1)(A0) if any extra terms are seen.
−3 (A1)(ft) (C1)
Note: Follow through from their part (a).
f′(x)=0 (M1)
Note: This may be implied from line below.
3a(−2)2−3=0 (M1)
(a=)14 (A1)(ft) (C3)
Note: Follow through from their part (a).
Examiners report
Many candidates could find the derivative of the cubic function and find the value of the derivative at x=0. For part (c) many candidates calculated the value of the function rather than the derivative at x=−2.
Many candidates could find the derivative of the cubic function and find the value of the derivative at x=0.
Many candidates could find the derivative of the cubic function and find the value of the derivative at x=0. For part (c) many candidates calculated the value of the function rather than the derivative at x=−2. However only the best realized that the derivative is zero at the maximum and so calculated the value of a.