| Date | May 2012 | Marks available | 4 | Reference code | 12M.1.sl.TZ1.3 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find and Show that | Question number | 3 | Adapted from | N/A |
Question
Let \(f(x) = {{\rm{e}}^{6x}}\) .
Write down \(f'(x)\) .
The tangent to the graph of f at the point \({\text{P}}(0{\text{, }}b)\) has gradient m .
(i) Show that \(m = 6\) .
(ii) Find b .
Hence, write down the equation of this tangent.
Markscheme
\(f'(x) = 6{{\rm{e}}^{6x}}\) A1 N1
[1 mark]
(i) evidence of valid approach (M1)
e.g. \(f'(0)\) , \(6{{\rm{e}}^{6 \times 0}}\)
correct manipulation A1
e.g. \(6{{\rm{e}}^0}\) , \(6 \times 1\)
\(m = 6\) AG N0
(ii) evidence of finding \(f(0)\) (M1)
e.g. \(y = {{\rm{e}}^{6(0)}}\)
\(b = 1\) A1 N2
[4 marks]
\(y = 6x + 1\) A1 N1
[1 mark]
Examiners report
On the whole, candidates handled this question quite well with most candidates correctly applying the chain rule to an exponential function and successfully finding the equation of the tangent line.
On the whole, candidates handled this question quite well with most candidates correctly applying the chain rule to an exponential function and successfully finding the equation of the tangent line. Some candidates lost a mark in (b)(i) for not showing sufficient working leading to the given answer.
On the whole, candidates handled this question quite well.
