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Date	May 2014	Marks available	4	Reference code	14M.1.sl.TZ2.15
Level	SL only	Paper	1	Time zone	TZ2
Command term	Write down	Question number	15	Adapted from	N/A

Question

A function is given as \(f(x) = 2{x^3} - 5x + \frac{4}{x} + 3,{\text{ }} - 5 \leqslant x \leqslant 10,{\text{ }}x \ne 0\).

Write down the derivative of the function.

[4]

Use your graphic display calculator to find the coordinates of the local minimum point of \(f(x)\) in the given domain.

[2]

Markscheme

\(6{x^2} - 5 - \frac{4}{{{x^2}}}\) (A1)(A1)(A1)(A1) (C4)

Note: Award (A1) for \(6{x^2}\), (A1) for \(–5\), (A1) for \(–4\), (A1) for \({x^{ - 2}}\) or \(\frac{1}{{{x^2}}}\).

Award at most (A1)(A1)(A1)(A0) if additional terms are seen.

[4 marks]

\((1.15,{\text{ }} 3.77)\) \(\left( {{\text{(1.15469..., 3.76980...)}}} \right)\) (A1)(A1) (C2)

Notes: Award (A1)(A1) for “\(x = 1.15\) and \(y = 3.77\)”.

Award at most (A0)(A1)(ft) if parentheses are omitted.

[2 marks]

Examiners report

[N/A]

Syllabus sections

Topic 7 - Introduction to differential calculus » 7.2 » The derivative of functions of the form \(f\left( x \right) = a{x^n} + b{x^{n - 1}} + \ldots \), where all exponents are integers.

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