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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.

Syllabus sections

Topic 2 - Functions and equations » 2.3
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