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Date May 2017 Marks available 3 Reference code 17M.1.sl.TZ2.6
Level SL only Paper 1 Time zone TZ2
Command term Find Question number 6 Adapted from N/A

Question

The values of the functions \(f\) and \(g\) and their derivatives for \(x = 1\) and \(x = 8\) are shown in the following table.

M17/5/MATME/SP1/ENG/TZ2/06

Let \(h(x) = f(x)g(x)\).

Find \(h(1)\).

[2]
a.

Find \(h'(8)\).

[3]
b.

Markscheme

expressing \(h(1)\) as a product of \(f(1)\) and  \(g(1)\)     (A1)

eg\(\,\,\,\,\,\)\(f(1) \times g(1),{\text{ }}2(9)\)

\(h(1) = 18\)     A1     N2

[2 marks]

a.

attempt to use product rule (do not accept \(h’ = f' \times g’\))     (M1)

eg\(\,\,\,\,\,\)\(h’ = fg' + gf',{\text{ }}h'(8) = f'(8)g(8) + g’(8)f(8)\)

correct substitution of values into product rule     (A1) 

eg\(\,\,\,\,\,\)\(h’(8) = 4(5) + 2( - 3),{\text{ }} - 6 + 20\)

\(h’(8) = 14\)     A1 N2

[3 marks]

b.

Examiners report

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

Syllabus sections

Topic 6 - Calculus » 6.2 » The product and quotient rules.
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