The Student Room Group
Reply 1
Your differentiation is fine.
What value does dydx\frac{dy}{dx} always take at stationary points? Can you use this fact to develop an equation which you can manipulate to give tan2x=3\tan 2x = 3?
You might also need to know the expression for tan2x\tan 2x in terms of sin2x\sin 2x and cos2x\cos 2x.
Reply 2
Stationary points occur when dy/dx = 0 i.e. 6cos 2x - 2sin 2x = 0

Now, so long as cos 2x doesn't equal 0 you can divide by it to get 6 = 2tan 2x or tan 2x = 3 as required.

To finish off, just confirm that IF cos 2x does equal 0 then you don't get a stationary point, i.e. you haven't inadvertently eliminated any stationary points by dividing by cos 2x.
Reply 3
Ah that makes perfect sense! Thanks so much! I'd never thought of asking for help on here before. I might become a regular :p: