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Date	November 2012	Marks available	3	Reference code	12N.1.sl.TZ0.15
Level	SL only	Paper	1	Time zone	TZ0
Command term	Find	Question number	15	Adapted from	N/A

Question

f (x) = 5x³ − 4x² + x

Find f'(x).

[3]

Find using your answer to part (a) the x-coordinate of

(i) the local maximum point;

(ii) the local minimum point.

[3]

Markscheme

15x² – 8x + 1 (A1)(A1)(A1) (C3)

Note: Award (A1) for each correct term.

[3 marks]

15x² – 8x +1 = 0 (A1)(ft)

Note: Award (A1)(ft) for setting their derivative to zero.

(i) \((x =)\frac{1}{5}(0.2)\) (A1)(ft)

(ii) \((x =)\frac{1}{3}(0.333)\) (A1)(ft) (C3)

Notes: Follow through from their answer to part (a).

[3 marks]

Examiners report

Many candidates lost 1 mark in part (a) through not realizing that the derivative of x is 1. As a consequence, 15x² – 8x proved to be a popular answer.

Very few candidates gained the marks in part (b) to find the maximum and minimum point. Although the question indicated to use their answer to part (a), very few candidates set the derivative to zero which would have given them 1 mark. It seemed as if many candidates were trying to use their calculators to find the coordinates but could not find which was the maximum and which was the minimum.

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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