IB Questionbank

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 $h(x) = f(x)g(x)$ .

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]

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]

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Syllabus sections

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

Show 37 related questions

17M.1.sl.TZ2.6a: Find $h(1)$ .
16M.1.sl.TZ1.10d: Let $h(x) = f(x) \times g(x)$ . Find the equation of the tangent to the graph of $h$ at...
16M.1.sl.TZ1.10c: Find $g(1)$ .
16M.1.sl.TZ1.10b: Write down $g'(1)$ .
16M.1.sl.TZ1.10a: Find $f'(1)$ .
16N.1.sl.TZ0.10c: (i) Find $h'(x)$ . (ii) Hence, show that $h'(\pi ) = \frac{{ - 21!}}{2}{\pi ^2}$ .
12N.1.sl.TZ0.10a: Find $f'(x)$ .
12M.1.sl.TZ2.10a: Use the quotient rule to show that...
12M.1.sl.TZ2.10b: Hence find the coordinates of B.
12M.1.sl.TZ2.10c: Given that the line $y = k$ does not meet the graph of f , find the possible values of k .
12N.1.sl.TZ0.10c: Let $h(x) = \frac{1}{{x(x + 1)}}$ . The area enclosed by the graph of h , the x-axis and...
08N.2.sl.TZ0.9a: Show that $f'(x) = {{\rm{e}}^{2x}}(2\cos x - \sin x)$ .
08M.2.sl.TZ2.9a: Show that $f'(x) = {{\rm{e}}^x}(1 - 2x - {x^2})$ .
10M.1.sl.TZ1.9a: Use the quotient rule to show that $f'(x) = \frac{{ - 1}}{{{{\sin }^2}x}}$ .
10M.1.sl.TZ1.9c: Find the value of p and of q.
10M.1.sl.TZ1.9b: Find $f''(x)$ .
10M.1.sl.TZ1.9d: Use information from the table to explain why there is a point of inflexion on the graph of f...
09N.2.sl.TZ0.2c: Let $h(x) = f(x) \times g(x)$ . Find $h'(x)$ .
09M.1.sl.TZ1.3: Let $f(x) = {{\rm{e}}^x}\cos x$ . Find the gradient of the normal to the curve of f at...
09M.1.sl.TZ2.8b: Let $h(x) = {{\rm{e}}^{ - 3x}}\sin \left( {x - \frac{\pi }{3}} \right)$ . Find the exact...
10M.2.sl.TZ1.3b: On the grid below, sketch the graph of $y = f'(x)$ .
10M.2.sl.TZ1.3a: Find $f'(x)$ .
10M.2.sl.TZ2.10b: Let $g(x) = {x^3}\ln (4 - {x^2})$ , for $- 2 < x < 2$ . Show that...
10M.2.sl.TZ2.10a(i) and (ii): Let P and Q be points on the curve of f where the tangent to the graph of f is parallel to...
10M.2.sl.TZ2.10c: Let $g(x) = {x^3}\ln (4 - {x^2})$ , for $- 2 < x < 2$ . Sketch the graph of $g'$ .
10M.2.sl.TZ2.10d: Let $g(x) = {x^3}\ln (4 - {x^2})$ , for $- 2 < x < 2$ . Consider $g'(x) = w$ ....
11N.2.sl.TZ0.10a: Sketch the graph of f .
11N.2.sl.TZ0.10c: Show that $f'(x) = \frac{{20 - 6x}}{{{{\rm{e}}^{0.3x}}}}$ .
11N.2.sl.TZ0.10b(i) and (ii): (i) Write down the x-coordinate of the maximum point on the graph of f . (ii) Write...
11N.2.sl.TZ0.10d: Find the interval where the rate of change of f is increasing.
11M.1.sl.TZ1.5a: Use the quotient rule to show that $g'(x) = \frac{{1 - 2\ln x}}{{{x^3}}}$ .
11M.1.sl.TZ1.5b: The graph of g has a maximum point at A. Find the x-coordinate of A.
11M.1.sl.TZ2.4: Let $h(x) = \frac{{6x}}{{\cos x}}$ . Find $h'(0)$ .
13M.1.sl.TZ1.3a: Find $f'(x)$ .
13M.1.sl.TZ2.10d: find the equation of the normal to the graph of $h$ at P.
14M.2.sl.TZ1.7: Let $f(x) = \frac{{g(x)}}{{h(x)}}$ , where...
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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

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