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Extrema: First Derivative Test

AP Calculus AB· difficulty 2/5

For f(x)=x3−3x2f(x) = x^3 - 3x^2, the critical points are at

  • A

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

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  • B

    x=−1x = -1 and x=3x = 3

  • C

    x=0x = 0 only

  • D

    x=1x = 1 and x=3x = 3

Explanation

f′(x)=3x2−6x=3x(x−2)=0⇒x=0,2f'(x) = 3x^2 - 6x = 3x(x - 2) = 0 \Rightarrow x = 0, 2.

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