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Date May 2019 Marks available 4 Reference code 19M.2.SL.TZ1.S_3
Level Standard Level Paper Paper 2 Time zone Time zone 1
Command term Find Question number S_3 Adapted from N/A

Question

Consider the function  f ( x ) = x 2 e 3 x ,   x R .

Find f ( x ) .

[4]
a.

The graph of f has a horizontal tangent line at x = 0 and at x = a . Find a .

[2]
b.

Markscheme

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

choosing product rule     (M1)

eg    u v + v u ( x 2 ) ( e 3 x ) + ( e 3 x ) x 2

correct derivatives (must be seen in the rule)      A1A1

eg    2 x 3 e 3 x

f ( x ) = 2 x e 3 x + 3 x 2 e 3 x     A1 N4

[4 marks]

a.

valid method    (M1)

eg    f ( x ) = 0

a = 0.667 ( = 2 3 )   (accept  x = 0.667 )     A1 N2

[2 marks]

b.

Examiners report

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

Syllabus sections

Topic 4—Statistics and probability » SL 4.1—Concepts, reliability and sampling techniques
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Topic 5—Calculus » AHL 5.9—Differentiating standard functions and derivative rules
Topic 4—Statistics and probability
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