17M.1.SL.TZ2.S_6

pestleMathematicsAISLPaper 117M· sl-5-3-differentiating-polynomials-n-e-zsource ↗

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]

Find $h'(8)$ .

[3]

Markscheme / solution

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

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]

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]

Examiners’ report

[N/A]