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Date	November 2016	Marks available	2	Reference code	16N.2.sl.TZ0.2
Level	SL only	Paper	2	Time zone	TZ0
Command term	Find	Question number	2	Adapted from	N/A

Question

Let $f(x) = 0.225{x^3} - 2.7x$ , for $- 3 \leqslant x \leqslant 3$ . There is a local minimum point at A.

On the following grid,

Find the coordinates of A.

[2]

(i) sketch the graph of $f$ , clearly indicating the point A;

(ii) sketch the tangent to the graph of $f$ at A.

N16/5/MATME/SP2/ENG/TZ0/02.b

[5]

Markscheme

${\text{A }}(2,{\text{ }}-3.6)$ A1A1 N2

[2 marks]

(i) (ii) N16/5/MATME/SP2/ENG/TZ0/02.b/M A1

A1A1A1 N4

A1 N1

Notes: (i) Award A1 for correct cubic shape with correct curvature.

Only if this A1 is awarded, award the following:

A1 for passing through their point A and the origin,

A1 for endpoints,

A1 for maximum.

(ii) Award A1 for horizontal line through their A.

[5 marks]

Examiners report

[N/A]

Syllabus sections

Topic 2 - Functions and equations » 2.2 » Function graphing skills.

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