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)=−x−2 (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.