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Math Help - Mean Value Theorem

  1. #1
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    Mean Value Theorem

    State the Mean Value theorem including all assumptions. Use it to prove that the function f(x)= (x^5-x+8)sin(xpi), has a critical point somewhere on the interval [0,1].
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  2. #2
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    Feel free to do that. Go ahead. State it.

    Then notice that:

    f(0)= (0^5-0+8)sin(0(pi)) = 8*0 = 0

    f(1)= (1^5-1+8)sin(1(pi)) = 8*0 = 0

    That's unusual. Is f(x) a constant function? Maybe we should appeal to ALL the criteria for the Mean Value Theorem.

    Note: Please stop posting problems with no work shown. Personally, I weary quickly of such laziness.
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