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# C3 DIFFERENTIATION edexcel q 2 jan 08 watch

1. 2. A curve C has equation
y=e^2x tanx

(a) Show that the turning points on C occur where tan x = −1.

Ive got the mark scheme but I can't see how the e^2x goes and i know the sec^2x = 1+ tanx^2 identity is used.

So far I have e^2x( 1+ tan^2 x + 2tanx)=0. How does the e^2x cancel

Quetsion:

http://http://www.edexcel.com/migrationdocuments/QP%20GCE%20Curriculum%202000/January%202008/6665_01_que_20080117.pdf

Mark scheme:

http://http://www.edexcel.com/migrationdocuments/QP%20GCE%20Curriculum%202000/January%202008/6665_01_rms_20080306.pdf

Thanks
2. the differential of tax is sec^2x
3. (Original post by SmileyGurl13)
the differential of tax is sec^2x
I know how to differentiate it but i can't see how the e^2x etc has been cancelled
4. u just divide by e^2x, then replace the sec^2 x with the formula u said. and factorise then solve.
5. divide both sides by e^2x
6. you need to differentiate it which gives e^2x(sec^2x+2tanx), then use the identity of tan and sec that gives you e^2x(tan^2x+2tanx+1) and then this means that the quadratic inside the brackets is equal to zero in the turning points. Therfore, x^2+2x+1 is (x+1)(x+1) factorised, this means that tanx=-1, there is a repeated solution, so tuning points only occur when tanx=-1.
7. when you get your expression, you make that equal 0, and as e^2x cannot equal 0, what's left in the brackets must equal 0
that's how it "disappears"
8. (Original post by MM1234)
I know how to differentiate it but i can't see how the e^2x etc has been cancelled
Well if it's a stationary point then dy/dx = 0 and e^x can never = 0 so you ignore it picture the graph
9. thanks
10. e^2x( 1+ tan^2 x + 2tanx)=0
Two things multiplied together = 0 so one of them equals 0

e^2x can't equal 0 (think of the graph of y=e^x)
so the bracket = 0 etc.
11. (Original post by crrrrrash)
i might be wrong but i think 1 + tanx = sec x, not 1+tan^2(x) = sec^2(x)
Nooooooo!

Learn these before your C3 exam.

You can't square root all three terms, only each side.
12. (Original post by tiny hobbit)
Nooooooo!

Learn these before your C3 exam.

You can't square root all three terms, only each side.
lol i did c3 last year, and today for some reason thought that the identity was 1 + tanx = secx, and thought that OP had done like the inverse of the mistake you thought i'd made
realised it like as soon as i'd done it and editted

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Updated: January 19, 2010
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