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Math Help - help finding the Maxima

  1. #1
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    help finding the Maxima

    I would be greatful for any help with the following problem. I know i need to find the dirivative of v and then from this i can transpose to find the unknown value of x. Just don't seem to be able!

    Q. The velocity, v, of a signal in a cable at a distance x is given by :

    v = K x ln (1/x) where 0<x<1 ( x is the algibraic x )

    where K is a positive constant. Find the value of x which gives the maximum velocity.

    Thanks again, James.

    Last edited by james jarvis; November 12th 2007 at 07:47 AM.
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  2. #2
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    NOT trying to bump, Just wanted to give it in the proper way.

    V = K x ln( \frac{1}{x} )
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  3. #3
    Bar0n janvdl's Avatar
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    Quote Originally Posted by james jarvis View Post
    NOT trying to bump, Just wanted to give it in the proper way.

    V = K x ln( \frac{1}{x} )
    You'll see that in every reply you post there will be a button that says "Edit", right next to "Quote"
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by james jarvis View Post
    NOT trying to bump, Just wanted to give it in the proper way.

    V = K x ln( \frac{1}{x} )
    \frac{dV}{dx} = K~ ln \left ( \frac{1}{x} \right ) + Kx \cdot \frac{1}{\frac{1}{x}} \cdot -\frac{1}{x^2}

    \frac{dV}{dx} = K~ ln \left ( \frac{1}{x} \right ) - K

    Set this equal to 0:
    K~ ln \left ( \frac{1}{x} \right ) - K = 0

    ln \left ( \frac{1}{x} \right ) - 1 = 0

    ln \left ( \frac{1}{x} \right ) = 1

    \frac{1}{x} = e

    x = \frac{1}{e}

    Is this a relative max or a relative min? I leave the answer to that question up to you.

    -Dan
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