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Date November 2009 Marks available 2 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]
a.

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

[1]
b.

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

[2]
c.

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]

a.

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

[1 mark]

b.

\(4x + 1 = 0\)     (M1)

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

[2 marks]

c.

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.

a.

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.

b.

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.

c.

Syllabus sections

Topic 7 - Introduction to differential calculus » 7.5 » Solution of \(f'\left( x \right) = 0\).
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