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Date May 2018 Marks available 1 Reference code 18M.1.SL.TZ2.T_14
Level Standard Level Paper Paper 1 Time zone Time zone 2
Command term Find Question number T_14 Adapted from N/A

Question

Consider the function f ( x ) = x 4 4 .

Find f'(x)

[1]
a.

Find the gradient of the graph of f at  x = 1 2 .

[2]
b.

Find the x-coordinate of the point at which the normal to the graph of f has gradient  1 8 .

[3]
c.

Markscheme

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

x3     (A1) (C1)

Note: Award (A0) for 4 x 3 4 and not simplified to x3.

[1 mark]

a.

( 1 2 ) 3      (M1)

Note: Award (M1) for correct substitution of 1 2  into their derivative.

1 8   (−0.125)     (A1)(ft) (C2)

Note: Follow through from their part (a).

[2 marks]

b.

x3 = 8     (A1)(M1)

Note: Award (A1) for 8 seen maybe seen as part of an equation y = 8x + c(M1) for equating their derivative to 8.

(x =) 2     (A1) (C3)

Note: Do not accept (2, 4).

[3 marks]

c.

Examiners report

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

Syllabus sections

Topic 5—Calculus » SL 5.1—Introduction of differential calculus
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Topic 5—Calculus » SL 5.3—Differentiating polynomials, n E Z
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Topic 2—Functions » SL 2.5—Modelling functions
Topic 2—Functions
Topic 5—Calculus

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