| Date | November 2013 | Marks available | 2 | Reference code | 13N.2.sl.TZ0.3 |
| Level | SL only | Paper | 2 | Time zone | TZ0 |
| Command term | Find | Question number | 3 | Adapted from | N/A |
Question
Let \(f(x) = \sqrt[3]{{{x^4}}} - \frac{1}{2}\).
Find \(f'(x)\).
[2]
a.
Find \(\int {f(x){\text{d}}x} \).
[4]
b.
Markscheme
expressing \(f\) as \({x^{\frac{4}{3}}}\) (M1)
\(f'(x) = \frac{4}{3}{x^{\frac{1}{3}}}{\text{ }}\left( { = \frac{4}{3}\sqrt[3]{x}} \right)\) A1 N2
[2 marks]
a.
attempt to integrate \({\sqrt[3]{{{x^4}}}}\) (M1)
eg \(\frac{{{x^{\frac{4}{3} + 1}}}}{{\frac{4}{3} + 1}}\)
\(\int {f(x){\text{d}}x = \frac{3}{7}{x^{\frac{7}{3}}} - \frac{x}{2} + c} \) A1A1A1 N4
[4 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
Syllabus sections
Topic 6 - Calculus » 6.2 » Derivative of \({x^n}\left( {n \in \mathbb{Q}} \right)\) , \(\sin x\) , \(\cos x\) , \(\tan x\) , \({{\text{e}}^x}\) and \(\ln x\) .
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