Mean Value Theorem and Extreme Value Theorem

AP Calculus AB· difficulty 2/5

For f(x)=x2f(x) = x^2 on (0,1)(0, 1) (open), the absolute extrema

  • A

    Min at x=0x = 0, max at x=1x = 1

  • B

    Don't exist

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  • C

    Are at x=0x = 0 and x=1x = 1

  • D

    Both at the midpoint

Explanation

Open interval — endpoints not included; sup and inf approach 00 and 11 but are never attained.

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