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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)=x510x2+15x6, xR.

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

d2ydx2=20x320     M1A1

for x>1, 20x320>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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