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Date May 2018 Marks available 2 Reference code 18M.2.sl.TZ1.1
Level SL only Paper 2 Time zone TZ1
Command term Find Question number 1 Adapted from N/A

Question

Let f(x) = ln x − 5x , for x > 0 .

Find f '(x).

[2]
a.

Find f "(x).

[1]
b.

Solve f '(x) = f "(x).

[2]
c.

Markscheme

\(f'\left( x \right) = \frac{1}{x} - 5\)     A1A1 N2

[2 marks]

a.

f "(x) = −x−2      A1 N1

[1 mark]

b.

METHOD 1 (using GDC)

valid approach      (M1)

eg 

0.558257

x = 0.558       A1 N2

Note: Do not award A1 if additional answers given.

 

METHOD 2 (analytical)

attempt to solve their equation f '(x) = f "(x)  (do not accept \(\frac{1}{x} - 5 =  - \frac{1}{{{x^2}}}\))      (M1)

eg  \(5{x^2} - x - 1 = 0,\,\,\frac{{1 \pm \sqrt {21} }}{{10}},\,\,\frac{1}{x} = \frac{{ - 1 \pm \sqrt {21} }}{2},\,\, - 0.358\)

0.558257

x = 0.558       A1 N2

Note: Do not award A1 if additional answers given.

[2 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 6 - Calculus » 6.2 » Derivative of \({x^n}\left( {n \in \mathbb{Q}} \right)\) , \(\sin x\) , \(\cos x\) , \(\tan x\) , \({{\text{e}}^x}\) and \(\ln x\) .
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