# Math Help - Could you help me some differentiation questions?

1. ## Could you help me some differentiation questions?

Find all points x where f achieves a local maximum or minimum for the
following functions (i.e. all the turning points). State whether f has local
maximum or local minimum at each point.

F(x) = (x^2 + 1) / (x^2 - 1)

I have got f'(x) = -4x / (x^2-1)^2

and then what should I do..? I also got f''(x) is {-4(x^2-1) + 16x^2(x^2-1)} / (x^2-1)^4
..But I don't know what I can do for next..

You should be able to tell that $(x^2- 1)^2$ is never negative so that the sign of $-4x/(x^2- 1)$ is the opposite of the sign of x. You don't really need to know the second derivative.