IB Questionbank

The following diagram shows part of the graph of $y = f(x)$ .

The graph has a local maximum at $A$ , where $x = - 2$ , and a local minimum at $B$ , where $x = 6$ .

Markscheme

A1A1A1A1 N4

Note: Award A1 for x-intercept in circle at $-2$ , A1 for x-intercept in circle at $6$ .

Award A1 for approximately correct shape.

Only if this A1 is awarded, award A1 for a negative y-intercept.

[4 marks]

$f''( - 2),{\text{ }}f'(6),{\text{ }}f(0)$ A2 N2

[2 marks]

Examiners report

Syllabus sections

Topic 6 - Calculus » 6.3 » Graphical behaviour of functions, including the relationship between the graphs of

$f$ ,

${f'}$ and

${f''}$ .

17M.1.sl.TZ1.6b: Determine the concavity of the graph of $f$ when $4 < x < 5$ and justify your answer.
17M.1.sl.TZ1.6a.ii: Find the equation of the normal to the curve of $f$ at P.
17M.1.sl.TZ1.6a.i: Write down the gradient of the curve of $f$ at P.
08M.2.sl.TZ1.5a: On the grid below, sketch a graph of $y = f''(x)$ , clearly indicating the x-intercept.
10M.1.sl.TZ2.7a: Write down the x-intercepts of the graph of the derivative function, $f'$ .
10M.1.sl.TZ2.7c: At point D on the graph of f , the x-coordinate is $- 0.5$ . Explain why $f''(x) < 0$ ...
10M.1.sl.TZ2.7b: Write down all values of x for which $f'(x)$ is positive.
09N.1.sl.TZ0.9c: Describe the behaviour of the graph of $f$ for large $|x|$ .
09M.1.sl.TZ1.4b: Write down the value of t when the velocity is greatest.
09M.1.sl.TZ1.4a: Complete the following table by noting which graph A, B or C corresponds to each function.
10N.2.sl.TZ0.7a: There are two points of inflexion on the graph of f . Write down the x-coordinates of these...
10N.2.sl.TZ0.7b: Let $g(x) = f''(x)$ . Explain why the graph of g has no points of inflexion.
13M.1.sl.TZ1.10d: There is a point of inflexion on the graph of $f$ at $x = \sqrt[4]{3}$ ...
14M.1.sl.TZ2.6b: Write down the following in order from least to greatest:...
15M.1.sl.TZ1.9b: The graph of $f$ has a point of inflexion when $x = 1$ . Show that $k = 3$ .
15M.2.sl.TZ1.10b: Write down $f'(2)$ .
15N.1.sl.TZ0.10a: Explain why the graph of $f$ has a local minimum when $x = 5$ .
15N.1.sl.TZ0.10b: Find the set of values of $x$ for which the graph of $f$ is concave down.

Date	May 2014	Marks available	4	Reference code	14M.1.sl.TZ2.6
Level	SL only	Paper	1	Time zone	TZ2
Command term	Sketch	Question number	6	Adapted from	N/A

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Markscheme

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