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Date	November 2009	Marks available	3	Reference code	09N.1.sl.TZ0.6
Level	SL only	Paper	1	Time zone	TZ0
Command term	Find	Question number	6	Adapted from	N/A

Question

Let \(f (x) = 2x^2 + x - 6\)

Find \(f'(x)\).

[3]

Find the value of \(f'( - 3)\).

[1]

Find the value of \(x\) for which \(f'(x) = 0\).

[2]

Markscheme

\(f'(x) = 4x + 1\) (A1)(A1)(A1) (C3)

Note: Award (A1) for each term differentiated correctly.

Award at most (A1)(A1)(A0) if any extra terms seen.

[3 marks]

\(f'( - 3) = - 11\) (A1)(ft) (C1)

[1 mark]

\(4x + 1 = 0\) (M1)

\(x = - \frac{{1}}{{4}}\) (A1)(ft) (C2)

[2 marks]

Examiners report

This was a fairly standard question. However, some candidates found f (−3) instead of \(f'\)(−3). Quite a few candidates were unable to answer part (c) as they tried to find \(f'\)(0) instead of finding x when \(f'\)(x) = 0.

Syllabus sections

Topic 7 - Introduction to differential calculus » 7.2 » The derivative of functions of the form \(f\left( x \right) = a{x^n} + b{x^{n - 1}} + \ldots \), where all exponents are integers.

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