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Date May 2017 Marks available 3 Reference code 17M.1.AHL.TZ1.H_12
Level Additional Higher Level Paper Paper 1 (without calculator) Time zone Time zone 1
Command term Show that Question number H_12 Adapted from N/A

Question

Consider the function q ( x ) = x 5 10 x 2 + 15 x 6 ,   x R .

Show that the graph of y = q ( x ) is concave up for x > 1 .

[3]
e.i.

Sketch the graph of y = q ( x ) showing clearly any intercepts with the axes.

[3]
e.ii.

Markscheme

d 2 y d x 2 = 20 x 3 20      M1A1

for x > 1 ,   20 x 3 20 > 0 concave up     R1AG

 

[3 marks]

e.i.

M17/5/MATHL/HP1/ENG/TZ1/B12.e.ii/M

x -intercept at ( 1 ,   0 )      A1

y -intercept at ( 0 ,   6 )      A1

stationary point of inflexion at ( 1 ,   0 ) with correct curvature either side     A1

[3 marks]

e.ii.

Examiners report

[N/A]
e.i.
[N/A]
e.ii.

Syllabus sections

Topic 5 —Calculus » SL 5.7—The second derivative
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Topic 5 —Calculus

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