Determining Concavity

AP Calculus AB· difficulty 3/5

For f(x)=x4f(x) = x^4, f(0)=0f''(0) = 0. Is x=0x = 0 an inflection point?

  • A

    Yes, because f(0)=0f''(0) = 0

  • B

    No — ff'' does not change sign at 00

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  • C

    Yes — ff has a max there

  • D

    Cannot tell

Explanation

f=12x20f'' = 12 x^2 \ge 0. No sign change → no inflection. (Just a min.)

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