IB Questionbank

recognizing need to find $f(2)$ or $f'(2)$ (R1)

$f(2) = \frac{{18}}{6}$ (seen anywhere) (A1)

correct substitution into the quotient rule (A1)

eg $\frac{{6(5) - 18(2)}}{{{6^2}}}$

$f'(2) = - \frac{6}{{36}}$ A1

gradient of normal is 6 (A1)

attempt to use the point and gradient to find equation of straight line (M1)

eg $y - f(2) = - \frac{1}{{f'(2)}}(x - 2)$

correct equation in any form A1 N4

eg $y - 3 = 6(x - 2),{\text{ }}y = 6x - 9$

[7 marks]

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

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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...
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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...
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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 .
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13M.1.sl.TZ1.3a: Find $f'(x)$ .
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Date	May 2014	Marks available	7	Reference code	14M.2.sl.TZ1.7
Level	SL only	Paper	2	Time zone	TZ1
Command term	Find	Question number	7	Adapted from	N/A

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