calculus

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Determine where the given function is concave up or where it is concave down:
f(x)=9x/x^2+49

  • calculus -

    f = 9x/(x^2 + 49)

    f is concave up where f'' > 0

    f' = -9(x^2 - 49) / (x^2 + 49)^2

    f'' = 18x(x^2 - 147)/(x^2 + 49)^3

    f'' < 0 where 0 < x < √147 or x < -√147
    f'' > 0 where -√147 < x < 0 or x > √147

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