Date | May 2021 | Marks available | 1 | Reference code | 21M.1.SL.TZ1.5 |
Level | Standard Level | Paper | Paper 1 (without calculator) | Time zone | Time zone 1 |
Command term | Find | Question number | 5 | Adapted from | N/A |
Question
Consider the functions f(x)=-(x-h)2+2k and g(x)=ex-2+k where h, k∈ℝ.
The graphs of f and g have a common tangent at x=3.
Find f'(x).
[1]
a.
Show that .
[3]
b.
Hence, show that .
[3]
c.
Markscheme
A1
[1 mark]
a.
OR (may be seen anywhere) A1
Note: The derivative of must be explicitly seen, either in terms of or .
recognizing (M1)
OR A1
Note: The final A1 is dependent on one of the previous marks being awarded.
AG
[3 marks]
b.
(M1)
correct equation in
EITHER
A1
A1
OR
A1
A1
THEN
AG
[3 marks]
c.
Examiners report
[N/A]
a.
[N/A]
b.
[N/A]
c.