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Mean Value Theorem and Extreme Value Theorem

AP Calculus AB· difficulty 3/5

For f(x)=x2f(x) = x^2 on [−1,2][-1, 2], find cc guaranteed by MVT.

  • A

    12\tfrac{1}{2}

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  • B

    22

  • C

    11

  • D

    32\tfrac{3}{2}

Explanation

Slope: (4−1)/(2−(−1))=1(4 - 1)/(2 - (-1)) = 1. f′(c)=2c=1⇒c=1/2f'(c) = 2c = 1 \Rightarrow c = 1/2.

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