| Date | November 2016 | Marks available | 3 | Reference code | 16N.2.sl.TZ0.4 |
| Level | SL only | Paper | 2 | Time zone | TZ0 |
| Command term | Find | Question number | 4 | Adapted from | N/A |
Question
Let \(f(x) = x{{\text{e}}^{ - x}}\) and \(g(x) = - 3f(x) + 1\).
The graphs of \(f\) and \(g\) intersect at \(x = p\) and \(x = q\), where \(p < q\).
Find the value of \(p\) and of \(q\).
[3]
a.
Hence, find the area of the region enclosed by the graphs of \(f\) and \(g\).
[3]
b.
Markscheme
valid attempt to find the intersection (M1)
eg\(\,\,\,\,\,\)\(f = g\), sketch, one correct answer
\(p = 0.357402,{\text{ }}q = 2.15329\)
\(p = 0.357,{\text{ }}q = 2.15\) A1A1 N3
[3 marks]
a.
attempt to set up an integral involving subtraction (in any order) (M1)
eg\(\,\,\,\,\,\)\(\int_p^q {\left[ {f(x) - g(x)} \right]{\text{d}}x,{\text{ }}} \int_p^q {f(x){\text{d}}x - } \int_p^q {g(x){\text{d}}x} \)
0.537667
\({\text{area}} = 0.538\) A2 N3
[3 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
