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Determine the concavity for f(x)= 4/x^2-1

I took the second derivative and solved for zeros. I got x=-1 and x=1. However when plugged into the orig. equation this results in 4/0 (undefined). Does this mean there is no concavity?

  • Concavity-Calculus -

    if f = 4/(x^2-1)
    f'' = 8(3x^2+1)/(x^2-1)^3
    f'' is never zero.
    f'' is discontinuous at x=1 and -1, and changes sign there

    so, f ix concave down for |x|<1 and concave up for |x|>1

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