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Date	May 2018	Marks available	3	Reference code	18M.1.sl.TZ2.14
Level	SL only	Paper	1	Time zone	TZ2
Command term	Find	Question number	14	Adapted from	N/A

Question

Consider the function $f\left( x \right) = \frac{{{x^4}}}{4}$ .

Find f'(x)

[1]

Find the gradient of the graph of f at $x = - \frac{1}{2}$ .

[2]

Find the x-coordinate of the point at which the normal to the graph of f has gradient ${ - \frac{1}{8}}$ .

[3]

Markscheme

x³ (A1) (C1)

Note: Award (A0) for $\frac{{4{x^3}}}{4}$ and not simplified to x³.

[1 mark]

${\left( { - \frac{1}{2}} \right)^3}$ (M1)

Note: Award (M1) for correct substitution of ${ - \frac{1}{2}}$ into their derivative.

${ - \frac{1}{8}}$ (−0.125) (A1)(ft) (C2)

Note: Follow through from their part (a).

[2 marks]

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]

Examiners report

[N/A]

Syllabus sections

Topic 7 - Introduction to differential calculus » 7.3 » Gradients of curves for given values of

$x$ .

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