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Mean Value Theorem and Extreme Value Theorem

AP Calculus AB· difficulty 3/5

x a b

If f(a)=f(b)=0f(a) = f(b) = 0 and ff is differentiable on (a,b)(a,b), then there exists c∈(a,b)c \in (a,b) where:

  • A

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

  • B

    f′′(c)=0f''(c) = 0

  • C

    c=(a+b)/2c = (a+b)/2

  • D

    f′(c)=0f'(c) = 0

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Explanation

Rolle's theorem guarantees a point where f′(c)=0f'(c) = 0.

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