Two questions (1 Viewer)

[GaDaMIt]

1) If f(x) = (x-2)²(x+4)³, show that f'(x) = (x-2)(x+4)²(5x+2)

any sort of shortcut to doing this?


and..

2) If f(x) = (x² - 4) / (x² - 1)
a) find f' (x) .. ive done this bit , its 6x / (x² - 1)²

b) Establish that f' (x) < 0 when x < 0 ( x =/= -1), and f'(x) > 0 when x > 0 ( x =/= 1)

c) State the equations of any horizontal or vertical asymptotes

 

[cbadvanced]

Dude, go and enjoy your Christmas + New Year
I'm only here cos cant sleep + bored

 

[Affinity]

1) Not really
2)b is obvious. c) vert asymtopes at x=-1,1, horizontal asymtopes at y=1 both sides.

 

[Riviet]

Observe that the function in 2) is an even function. This should help you with b.

 

[powcy]

I wouldn't think that as the worst questions... as Riviet said, part b of Q2 clearly hints at the function being an even one.
As for the last part of that question, I think I did it by the whole limit as x approaches infinifty thing. I've always liked that for some reason...
And for the first part, Affinity is right... that question is worth more than one mark, I'm sure, and if so would have no "short-cut" of solving it. It doesn't take that much work anyway, just have to be a little careful.
Have a safe holiday, everyone! And hopefully all the offers work out for you!