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Math Help - Mean Value Theorem Question

  1. #1
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    Mean Value Theorem Question

    I am stuck on this one problem that is due in 45 minutes. If somebody could help me out I'd greatly appreciate it.




    Find all numbers c that satisfy the conclusion of the Mean Value Theorem for the following function and interval.

    f(x)=4x^3+4x-9, [0,2]
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  2. #2
    MHF Contributor red_dog's Avatar
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    The conclusion in Mean Value Theorem is that exists c\in(0,2) such that
    \displaystyle\frac{f(2)-f(0)}{2}=f'(c)
    That means
    \displaystyle f'(c)=20\Rightarrow 12c^2+4=20\Rightarrow c^2=\frac{4}{3}\Rightarrow c=\frac{2\sqrt{3}}{3}
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  3. #3
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    Quote Originally Posted by red_dog View Post
    The conclusion in Mean Value Theorem is that exists c\in(0,2) such that
    \displaystyle\frac{f(2)-f(0)}{2}=f'(c)
    That means
    \displaystyle f'(c)=20\Rightarrow 12c^2+4=20\Rightarrow c^2=\frac{4}{3}\Rightarrow c=\frac{2\sqrt{3}}{3}
    Thank you for the fast reply. We enter our homework online, and I did that exact same work. However, for whatever reason, the computer thought the square root of 4/3 was incorrect. Your answer it took, though. Thanks again.
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Geist View Post
    Thank you for the fast reply. We enter our homework online, and I did that exact same work. However, for whatever reason, the computer thought the square root of 4/3 was incorrect. Your answer it took, though. Thanks again.
    Probably because \sqrt{\frac{4}{3}} is not considered to be fully simplified, both because of the \sqrt{4} and the radical in the denominator.

    -Dan
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