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Fundamental Theorem of Calculus and Accumulation Functions

AP Calculus AB· difficulty 4/5

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Let F(x)=∫0xf(t) dtF(x) = \int_0^x f(t)\,dt where ff is shown (linear V-shape with ff first decreasing then increasing). FF has an inflection point where:

  • A

    ff is at a maximum

  • B

    f=0f = 0

  • C

    F=0F = 0

  • D

    ff has its minimum (kink)

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Explanation

Inflection points of FF occur where F′′=f′F'' = f' changes sign, i.e., where the slope of ff changes (the kink of the V).

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