Date | May 2018 | Marks available | 2 | Reference code | 18M.2.sl.TZ1.1 |
Level | SL only | Paper | 2 | Time zone | TZ1 |
Command term | Solve | 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′(x)=1x−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 1x−5=−1x2) (M1)
eg 5x2−x−1=0,1±√2110,1x=−1±√212,−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.