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Date November 2009 Marks available 4 Reference code 09N.1.sl.TZ0.5
Level SL only Paper 1 Time zone TZ0
Command term Find Question number 5 Adapted from N/A

Question

Consider \(f(x) = {x^2} + \frac{p}{x}\) , \(x \ne 0\) , where p is a constant.

Find \(f'(x)\) .

[2]
a.

There is a minimum value of \(f(x)\) when \(x = - 2\) . Find the value of \(p\) .

[4]
b.

Markscheme

\(f'(x) = 2x - \frac{p}{{{x^2}}}\)     A1A1     N2

Note: Award A1 for \(2x\) , A1 for \( - \frac{p}{{{x^2}}}\) .

[2 marks]

a.

evidence of equating derivative to 0 (seen anywhere)     (M1)

evidence of finding \(f'( - 2)\) (seen anywhere)     (M1)

correct equation     A1

e.g. \( - 4 - \frac{p}{4} = 0\) , \( - 16 - p = 0\)

\(p = - 16\)     A1     N3

[4 marks]

b.

Examiners report

Candidates did well on (a).

a.

For (b), a great number of candidates substituted into the function instead of into the derivative.

The derivate of \({x^2}\) was calculated without difficulties, but there were numerous problems regarding the derivative of \(\frac{p}{x}\) . There were several candidates who considered both p and x as variables; some tried to use the quotient rule and had difficulties, others used negative exponents and were not successful.

b.

Syllabus sections

Topic 6 - Calculus » 6.3 » Local maximum and minimum points.
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