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Math Help - Mean value theorum help?

  1. #1
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    Mean value theorum help?

    Find all numbers c that satisfy the conclusion of the Mean Value Theorem.
    so f(x)=e ^ -2x [0,3]
    using f(b)-f(a)=f'(c)(b-a)
    so that's
    f'(x) = 2e^-2x
    e^-2(3)-e^-2(0) = 2e^-2x(3-0)
    e^-6-1=3e^-2x
    now how do i solve for x?
    the ^ means exponent,
    the latex tags won't turn it into an exponent, how weird...
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  2. #2
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    Quote Originally Posted by dorkymichelle View Post
    e^-6-1=3e^-2x
    now how do i solve for x?
    Is this your equation?

    e^{-6}-1=3e^{-2x}

    If so divide both sides by 3, take the natural log of both sides and then divide both sides by -2
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  3. #3
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    Quote Originally Posted by dorkymichelle View Post
    Find all numbers c that satisfy the conclusion of the Mean Value Theorem.
    so f(x)=e^-2x [0,3]
    using f(b)-f(a)=f'(c)(b-a)
    so that's
    f'(x) = 2e^-2x
    e^-2(3)-e^-2(0) = 2e^-2x(3-0)
    e^-6-1=3e^-2x
    now how do i solve for x?
    f'(x) = -2e^{-2x}

    \frac{e^{-6} - 1}{3} = -2e^{-2x}<br />

    \frac{1 - e^{-6}}{6} = e^{-2x}

    log of both sides ... then isolate x
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