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Date	May 2008	Marks available	3	Reference code	08M.1.sl.TZ1.3
Level	SL only	Paper	1	Time zone	TZ1
Command term	Find	Question number	3	Adapted from	N/A

Question

Consider the function \(f(x) = 2{x^3} - 5{x^2} + 3x + 1\).

Find \(f'(x)\).

[3]

Write down the value of \(f'(2)\).

[1]

Find the equation of the tangent to the curve of \(y = f(x)\) at the point \((2{\text{, }}3)\).

[2]

Markscheme

\(f'(x) = 6{x^2} - 10x + 3\) (A1)(A1)(A1) (C3)

Notes: Award (A1) for each correct term and no extra terms.
Award (A1)(A1)(A0) if each term correct and extra term seen.
Award(A1)(A0)(A0) if two terms correct and extra term seen.
Award (A0) otherwise.

[3 marks]

\(f'(2) = 7\) (A1)(ft) (C1)

[1 mark]

\(y = 7x - 11\) or equivalent (A1)(ft)(A1)(ft) (C2)

Note: Award (A1)(ft) on their (b) for \(7x\) (must have \(x\)), (A1)(ft) for \( - 11\). Accept \(y - 3 = 7(x - 2)\) .

[2 marks]

Examiners report

Most candidates were able to score full marks for parts (a) and (b). When mistakes were made in part (a) follow-through marks could be awarded for part (b) provided working was shown. Part (c) was disappointing with many candidates not realizing that the answer in (b) was the gradient of the tangent line.

Syllabus sections

Topic 7 - Introduction to differential calculus » 7.2 » The derivative of functions of the form \(f\left( x \right) = a{x^n} + b{x^{n - 1}} + \ldots \), where all exponents are integers.

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