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Mean Value Theorem and Extreme Value Theorem

AP Calculus AB· difficulty 2/5

Rolle's theorem (special case of MVT) states that if ff is continuous on [a,b][a,b], differentiable on (a,b)(a,b), and f(a)=f(b)f(a) = f(b), then there is cc with

  • A

    f′(c)=0f'(c) = 0

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  • B

    f′′(c)=0f''(c) = 0

  • C

    f(c)=f(a)f(c) = f(a)

  • D

    f(c)=0f(c) = 0

Explanation

Rolle's: f′(c)=0f'(c) = 0.

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