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Math Help - Could you help me some differentiation questions?

  1. #1
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    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..

    Please help me
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  2. #2
    MHF Contributor

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    Re: Could you help me some differentiation questions?

    Whoever gave you these problems expects you to know that at a maximum, the first derivative goes from + (going upward) to - (going downward) and so must be 0 at the maximum. Similarly, at a minimum, the first derivative goes from - (going downward) to + (going upward) and so must be 0 at the minimum.

    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.
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