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Date November 2017 Marks available 7 Reference code 17N.1.SL.TZ0.S_6
Level Standard Level Paper Paper 1 (without calculator) Time zone Time zone 0
Command term Find Question number S_6 Adapted from N/A

Question

Let f ( x ) = 15 x 2 , for x R . The following diagram shows part of the graph of f and the rectangle OABC, where A is on the negative x -axis, B is on the graph of f , and C is on the y -axis.

N17/5/MATME/SP1/ENG/TZ0/06

Find the x -coordinate of A that gives the maximum area of OABC.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

attempt to find the area of OABC     (M1)

eg OA × OC,  x × f ( x ) ,   f ( x ) × ( x )

correct expression for area in one variable     (A1)

eg area = x ( 15 x 2 ) ,   15 x x 3 ,   x 3 15 x

valid approach to find maximum area (seen anywhere)     (M1)

eg A ( x ) = 0

correct derivative     A1

eg 15 3 x 2 ,   ( 15 x 2 ) + x ( 2 x ) = 0 ,   15 + 3 x 2

correct working     (A1)

eg 15 = 3 x 2 ,   x 2 = 5 ,   x = 5

x = 5   ( accept A ( 5 ,   0 ) )     A2     N3

[7 marks]

Examiners report

[N/A]

Syllabus sections

Topic 5 —Calculus » SL 5.8—Testing for max and min, optimisation. Points of inflexion
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Topic 5 —Calculus

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