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Question

Let $f(x) = \sqrt[3]{{{x^4}}} - \frac{1}{2}$ .

Find $f'(x)$ .

[2]

Find $\int {f(x){\text{d}}x}$ .

[4]

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]

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]

[N/A]

${x^n}\left( {n \in \mathbb{Q}} \right)$ ,

$\sin x$ ,

$\cos x$ ,

$\frac{1}{x}$ and

${{\text{e}}^x}$ .