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Determining Concavity

AP Calculus AB· difficulty 3/5

For f(x)=x4−4x3f(x) = x^4 - 4x^3, the xx-coordinates of inflection points are

  • A

    x=3x = 3 only

  • B

    x=2x = 2 only

  • C

    x=0x = 0 only

  • D

    x=0x = 0 and x=2x = 2

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Explanation

f′′=12x2−24x=12x(x−2)=0⇒x=0,2f'' = 12x^2 - 24x = 12x(x - 2) = 0 \Rightarrow x = 0, 2. Both are sign changes.

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