Mean Value Theorem and Extreme Value Theorem

AP Calculus AB· difficulty 3/5

x a b c

By the Mean Value Theorem, f(c)f'(c) equals:

  • A

    f(b)f(a)f'(b)-f'(a)

  • B

    f(b)f(a)f(b)-f(a)

  • C

    f(b)f(a)ba\dfrac{f(b)-f(a)}{b-a}

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  • D

    baf(b)f(a)\dfrac{b-a}{f(b)-f(a)}

Explanation

The MVT guarantees a cc where f(c)f'(c) equals the average rate of change f(b)f(a)ba\frac{f(b)-f(a)}{b-a}.

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