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Extrema: First Derivative Test

AP Calculus AB· difficulty 2/5

Given f′(x)=(x−1)(x−3)2f'(x) = (x-1)(x-3)^2, ff has a local extremum at

  • A

    x=1x = 1 only

    check_circle
  • B

    x=3x = 3 only

  • C

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

  • D

    Nowhere

Explanation

Sign change of f′f' only at x=1x = 1 (x=3x = 3 is a double root, no sign change). f′f' goes from −- to ++ at x=1x = 1 → local min.

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