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Determining Concavity

AP Calculus AB· difficulty 3/5

For f(x)=x4f(x) = x^4, f′′(0)=0f''(0) = 0 but 00 is <strong>not</strong> an inflection point because

  • A

    All of the above

  • B

    f′(0)=0f'(0) = 0

  • C

    ff is not differentiable at 00

  • D

    f′′f'' does not change sign at 00

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Explanation

Inflection requires sign change of f′′f''. f′′f'' stays ≥0\ge 0 on both sides of 00.

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