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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)=421xg(x)=421x , x0x0 .

(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=421x21x=421x

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

y2=2ln2(x1)(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.

Syllabus sections

Topic 6 - Core: Calculus » 6.1 » Finding equations of tangents and normals.
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