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Date None Specimen Marks available 3 Reference code SPNone.1.sl.TZ0.7
Level SL only Paper 1 Time zone TZ0
Command term Write down Question number 7 Adapted from N/A

Question

Given that f(x)=1x , answer the following.

Find the first four derivatives of f(x) .

[4]
a.

Write an expression for f(n)(x) in terms of x and n .

[3]
b.

Markscheme

f(x)=x2 (or 1x2 )     A1     N1

f (or \frac{2}{{{x^3}}} )     A1     N1

f'''(x) = - 6{x^{ - 4}} (or - \frac{6}{{{x^4}}} )     A1     N1

{f^{(4)}}(x) = 24{x^{ - 5}} (or \frac{{24}}{{{x^5}}} )     A1     N1

[4 marks]

a.

{f^{(n)}}(x) = \frac{{{{( - 1)}^n}n!}}{{{x^{n + 1}}}} or {( - 1)^n}n!({x^{ - (n + 1)}})     A1A1A1     N3

[3 marks]

b.

Examiners report

[N/A]
a.
[N/A]
b.

Syllabus sections

Topic 6 - Calculus » 6.2 » Extension to higher derivatives.

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