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help with question from specimen paper

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I have never come across a question like this, anyone have any idea as to how to solve it?

My main problem is with question a.I have found a(i) but i don't know how to solve a(ii).

[img]http://img.photobucket.com/albums/v625/deadflappin/MathSLSpecimen2006_Page_34.jpg[/img]

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Anyways for

(a) (i) the vertical distance p would just be g(x) - f(a)
(ii) Since you have the equation for "p", then just take a derivative and test for a maximum

p=10x+1-e^2x
p'=10-2e^2x
10-2e^2x=0
2e^2x=10
e^2x=5
2x=ln5
x=ln5/2
x is about .805
p'(.5)=+ (increasing)
p'(1)=- (decreasing)
Maximum at x=.805

Also, I was looking for some specimen papers. Do you know where I can get some? Edited by PuLsE

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For math, there is only one specimen paper for HL and one for SL. For the new syllabus, you can get P1 and P2 of M08 (TZ1&TZ2) pretty soon though >.<

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