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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]
a.

(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]
b.

Markscheme

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

[2 marks]

a.

(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]

b.

Examiners report

[N/A]
a.
[N/A]
b.

Syllabus sections

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