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Date	May 2017	Marks available	2	Reference code	17M.2.sl.TZ1.3
Level	SL only	Paper	2	Time zone	TZ1
Command term	Find	Question number	3	Adapted from	N/A

Question

Consider the graph of $f(x) = \frac{{{{\text{e}}^x}}}{{5x - 10}} + 3$ , for $x \ne 2$ .

Find the $y$ -intercept.

[2]

Find the equation of the vertical asymptote.

[2]

Find the minimum value of $f(x)$ for $x > 2$ .

[2]

Markscheme

valid approach (M1)

eg $\,\,\,\,\,$ $f(0)$ , M17/5/MATME/SP2/ENG/TZ1/03.a/M

$y$ -intercept is 2.9 A1 N2

[2 marks]

valid approach involving equation or inequality (M1)

eg $\,\,\,\,\,$ $5x - 10 = 0,{\text{ }}2,{\text{ }}x \ne 2$

$x = 2$ (must be an equation) A1 N2

[2 marks]

7.01710

${\text{min value}} = 7.02$ A2 N2

Note: If candidate gives the minimum point as their final answer, award A1 for $(3,{\text{ }}7.02)$ .

[2 marks]

Examiners report

[N/A]

Syllabus sections

Topic 2 - Functions and equations » 2.2

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SPNone.2.sl.TZ0.2b: On the grid below, sketch the graph of f .
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12M.1.sl.TZ2.10c: Given that the line $y = k$ does not meet the graph of f , find the possible values of k .
17M.1.sl.TZ2.10b: Show that the $x$ -coordinate of B is $- \frac{k}{2}$ .
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17N.1.sl.TZ0.3b.ii: Write down ${f^{ - 1}}(2)$ .
12N.2.sl.TZ0.3b: Write down the gradient of the curve at P.
12N.2.sl.TZ0.7a: On the grid below, sketch the graph of $s$ .
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10N.2.sl.TZ0.8b: The graph of f has a maximum value when $x = c$ . Find the value of c .
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10M.2.sl.TZ2.6a: Write down the x-coordinate of A.
10M.2.sl.TZ2.5a: On the diagram above, sketch the graph of g.
10M.2.sl.TZ2.5b: Solve $f(x) = g(x)$ .
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11N.2.sl.TZ0.10c: Show that $f'(x) = \frac{{20 - 6x}}{{{{\rm{e}}^{0.3x}}}}$ .
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16M.1.sl.TZ2.1b: Write down the value of $a$ and of $b$ .
17M.1.sl.TZ1.9b: Find the value of $a$ .
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17M.2.sl.TZ2.8a: Find the value of $p$ .
17M.2.sl.TZ2.8b.ii: Write down the rate of change of $f$ at A.
17N.1.sl.TZ0.3b.i: Write down $f(2)$ ;

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