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Determining Concavity

AP Calculus AB· difficulty 3/5

For y=11+x2y = \dfrac{1}{1 + x^2} (a common bell-shape), inflection points occur at x=x =

  • A

    ±3\pm \sqrt 3

  • B

    00

  • C

    ±1\pm 1

  • D

    ±1/3\pm 1/\sqrt 3

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Explanation

Standard result: y′′=(6x2−2)/(1+x2)3=0y'' = (6x^2 - 2)/(1+x^2)^3 = 0 when x=±1/3x = \pm 1/\sqrt 3.

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