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Find the first and second derivative of the function
Use the information about the derivatives to determine any local maxima and minima, regions where the curve iss concave up or down, and any inflection points

  • math -

    y = x^3/(1-x^2)
    y' = -x^2(x-3)/(1-x^2)^2
    y'' = -2x(x^2+3)/(1-x^2)^3

    since the denominator is always positive or 0, y' and y'' are zero when the numerators are zero, and undefined at x=±1.

    Now it should be easy to read off the increasing/decreasing/concavity intervals.

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