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Math Help - stationary points question

  1. #1
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    stationary points question

    "find the stationary points of the following curves and determine whether the points are maxima, minima, or points of inflexion"

    y= (x + 1)/ (x - 1)


    I know how to these sorts of questions but for this example i find it tricky, I set it as:

    y= (x + 1) (x - 1)^-1 but then differentiating this is tricky - not sure how to use the chain rule on the latter, or the product rule overall.

    thanks for any help.
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  2. #2
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    Quote Originally Posted by porge111 View Post
    "find the stationary points of the following curves and determine whether the points are maxima, minima, or points of inflexion"

    y= (x + 1)/ (x - 1)


    I know how to these sorts of questions but for this example i find it tricky, I set it as:

    y= (x + 1) (x - 1)^-1 but then differentiating this is tricky - not sure how to use the chain rule on the latter, or the product rule overall.

    thanks for any help.
    In this case I would use the quotient rule:

    f(x) = \dfrac{u(x)}{v(x)}~\implies~f'(x)=\dfrac{v(x) \cdot u'(x) - u(x) \cdot v'(x)}{(v(x))^2}

    You should come out with: f'(x)=-\dfrac2{(x-1)^2}
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