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Date May 2010 Marks available 3 Reference code 10M.2.sl.TZ1.3
Level SL only Paper 2 Time zone TZ1
Command term Find Question number 3 Adapted from N/A

Question

Let \(f(x) = x\cos x\) , for \(0 \le x \le 6\) .

Find \(f'(x)\) .

[3]
a.

On the grid below, sketch the graph of \(y = f'(x)\) .


[4]
b.

Markscheme

evidence of choosing the product rule     (M1)

e.g. \(x \times ( - \sin x) + 1 \times \cos x\)

\(f'(x) = \cos x - x\sin x\)     A1A1     N3

[3 marks]

a.


     A1A1A1A1     N4

Note: Award A1 for correct domain, \(0 \le x \le 6\) with endpoints in circles, A1 for approximately correct shape, A1 for local minimum in circle, A1 for local maximum in circle.

[4 marks]

b.

Examiners report

This problem was well done by most candidates. There were some candidates that struggled to apply the product rule in part (a) and often wrote nonsense like \( - x\sin x = - \sin {x^2}\) .

a.

In part (b), few candidates were able to sketch the function within the required domain and a large number of candidates did not have their calculator in the correct mode.

b.

Syllabus sections

Topic 2 - Functions and equations » 2.2 » Use of technology to graph a variety of functions, including ones not specifically mentioned.
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