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Date	November 2009	Marks available	1	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 » 7.3 » Gradients of curves for given values of

$x$ .

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