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Math Help - Calculus problem

  1. #1
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    Calculus problem

    Let f:[-1,8] -> R be a differentiable function such that f(-1)=1,f(8)=10,

    then there always exists c1, c2 and c3
    Є (-1,8) such that f'(c1) + f'(c2) + f'(c3) = k, then k is equal to _______
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  2. #2
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    I'm able to get this problem up to certain point, but then I doubt when adding the c's.

    So by the Mean Value Theorem you have:

    f'(c) = (f(b) - f(a))/(b-a)

    the interval [-1,8] is your [a,b] so pluging in with your givens you should get f'(c) = 1

    But after that I doubt my answer, I would suggest that c1=c2=c3, thus for k you get 3

    But I will like some confirmation though.
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  3. #3
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    it is given that c1,c2 and c3 are not equal
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