Date | May 2009 | Marks available | 7 | Reference code | 09M.1.hl.TZ1.7 |
Level | HL only | Paper | 1 | Time zone | TZ1 |
Command term | Find | Question number | 7 | Adapted from | N/A |
Question
Consider the functions f and g defined by f(x)=21xf(x)=21x and g(x)=4−21xg(x)=4−21x , x≠0x≠0 .
(a) Find the coordinates of P, the point of intersection of the graphs of f and g .
(b) Find the equation of the tangent to the graph of f at the point P.
Markscheme
(a) 21x=4−21x21x=4−21x
attempt to solve the equation M1
x = 1 A1
so P is (1, 2) , as f(1)=2f(1)=2 A1 N1
(b) f′(x)=−1x221xln2 A1
attempt to substitute x-value found in part (a) into their f′(x) M1
f′(1)=−2ln2
y−2=−2ln2(x−1)(or equivalent) M1A1 N0
[7 marks]
Examiners report
Most candidates answered part (a) correctly although some candidates showed difficulty solving the equation using valid methods. Part (b) was less successful with many candidates failing to apply chain rule to obtain the derivative of the exponential function.