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Extrema: First Derivative Test

AP Calculus AB· difficulty 3/5

x f'

The graph of f′f' is positive before x=cx=c and positive after, with f′(c)=0f'(c)=0 at the peak. Then at x=cx=c, ff has:

  • A

    Local maximum

  • B

    Local minimum

  • C

    Inflection point with horizontal tangent

  • D

    No extremum

    check_circle

Explanation

Wait: rereading—if f′f' is shown going up to peak (positive) then down to zero. Hmm. At the peak of f′f', f′(c)f'(c) can be positive (no sign change of f′f'), so ff has no extremum at cc.

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