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Math Help - Find the number c that satisfies the conclusion of the mean value theorem.

  1. #1
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    Find the number c that satisfies the conclusion of the mean value theorem.

    f(x) = x / (x+ 4) [1,8]

    I found fprime(x) to be 4/(x+4)^2
    Then I used (f(b) - f(a)) / (b -a) and found that to be 7/15

    I set the equation to zero to solve for c and my answer comes out wrong. (squarroot60/7)-4
    PS How do I use the math syntax keys on this forum?
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  2. #2
    Senior Member apcalculus's Avatar
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    Pretty sure f(b) - f(a) equals 7/15 here. When you divide by (b-a), you get 1/15.

    The derivative looks good.

    I hope this helps! Good luck!
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  3. #3
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    Set what equation to 0? The mean value theorem says that there exist some c such that
    f'(c)= \frac{f(8)- f(1)}{8- 1}

    f(8)- f(1)= 7/15. (f(8- f(1)/(9- 1)= 1/15. You want to set \frac{x}{x+ 4}= \frac{1}{15}.
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  4. #4
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    2/7 ?
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  5. #5
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    still not sure what I'm doing wrong, the answer i submit is wrong :/
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  6. #6
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    HallsofIvy was correct up until this point:

    You want to set \frac{x}{x+4}=\frac{1}{15}.
    You actually want to set f'(c)=\frac{4}{(c+4)^{2}}=\frac{1}{15}.

    [EDIT]: I'm sure that was a "thought-o" on HallsofIvy's part.
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  7. #7
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     \sqrt{60} -4 = c

    ??
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  8. #8
    A Plied Mathematician
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    Your answer is correct. I would show the steps of rejecting the inadmissible solution when you take the square root.

    I think you're done!
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