| Date | November 2007 | Marks available | 3 | Reference code | 07N.1.sl.TZ0.15 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 15 | Adapted from | N/A |
Question
A function is represented by the equation
\[f(x) = a{x^2} + \frac{4}{x} - 3\]
Find \(f ′(x)\) .
The function \(f (x)\) has a local maximum at the point where \(x = −1\).
Find the value of a.
Markscheme
\(f(x) = a{x^2} + 4{x^{ - 1}} - 3\)
\(f'(x) = 2ax - 4{x^{ - 2}}\) (A3)
(A1) for 2ax, (A1) for –4x –2 and (A1) for derivative of –3 being zero. (C3)
[3 marks]
\(2ax - 4x^{-2} = 0\) (M1)
\(2a( - 1) - 4{( - 1)^{ - 2}} = 0\) (M1)
\( -2a - 4 = 0\)
\(a = -2\) (A1)(ft)
(M1) for setting derivative function equal to 0. (M1) for inserting \(x = -1\) but do not award (M0)(M1) (C3)
[3 marks]
Examiners report
(a) Many candidates gave up at this point. Those who attempted the derivative did so with varying success. Many could not differentiate a term with a negative index.
(b) In part (b) most substituted the -1 into the original function rather than the differentiated one. They did not realize they had to put the differentiated function equal to zero.
