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Date	May 2016	Marks available	3	Reference code	16M.1.sl.TZ2.15
Level	SL only	Paper	1	Time zone	TZ2
Command term	Find	Question number	15	Adapted from	N/A

Question

Consider the function $f(x) = {x^3} - 3{x^2} + 2x + 2$ . Part of the graph of $f$ is shown below.

Find $f'(x)$ .

[3]

There are two points at which the gradient of the graph of $f$ is $11$ . Find the $x$ -coordinates of these points.

[3]

Markscheme

$(f'(x) = )\,\,3{x^2} - 6x + 2$ (A1)(A1)(A1) (C3)

Note: Award (A1) for $3{x^2}$ , (A1) for $- 6x$ and (A1) for $+ 2$ .
Award at most (A1)(A1)(A0) if there are extra terms present.

$11 = 3{x^2} - 6x + 2$ (M1)

Note: Award (M1) for equating their answer from part (a) to $11$ , this may be implied from $0 = 3{x^2} - 6x - 9$ .

$(x = )\,\, - 1\,\,,\,\,\,\,(x = )\,\,3$ (A1)(ft)(A1)(ft) (C3)

Note: Follow through from part (a).
If final answer is given as coordinates, award at most (M1)(A0)(A1)(ft) for $( - 1,\,\, - 4)$ and $(3,\,\,8)$ .

Examiners report

Question 15: Differential calculus.

Many candidates correctly differentiated the cubic equation. Most candidates were unable to use differential calculus to find the point where a cubic function had a specified gradient.

Question 15: Differential calculus.

Many candidates correctly differentiated the cubic equation. Most candidates were unable to use differential calculus to find the point where a cubic function had a specified gradient.

Syllabus sections

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

$x$ .

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