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Second Derivative Test

AP Calculus AB· difficulty 3/5

For f(x)=x3−3x2f(x) = x^3 - 3x^2, the inflection point is at

  • A

    x=2x = 2

  • B

    No inflection

  • C

    x=0x = 0

  • D

    x=1x = 1

    check_circle

Explanation

f′′=6x−6=0⇒x=1f'' = 6x - 6 = 0 \Rightarrow x = 1. f′′f'' changes sign there.

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