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Math Help - find the number of solution of this ln equation

  1. #16
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    you are correct it will be negative for every X.

    so its a maximum point

    so the derivative before point x=1/a is positive
    ans the derivative after point x=1/a in negative.
    by i cant see where we got two negative point with a poisitive point in the middle
    ??
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  2. #17
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    Quote Originally Posted by transgalactic View Post
    you are correct it will be negative for every X.

    so its a maximum point

    so the derivative before point x=1/a is positive
    ans the derivative after point x=1/a in negative.
    by i cant see where we got two negative point with a poisitive point in the middle
    ??
    i dont know how to get it??
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  3. #18
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    Quote Originally Posted by transgalactic View Post
    i dont know how to get it??
    Let's consider a simple example y = 1 - x^2. Now it's maximum is located at x = 1 and it's 1 (>0). As x \to \pm \infty then y \to - \infty so there must be two places (at least) where y = - #, one for x > 0 and one for x < 0. In this case, I'll choose x = -2,\; \text{and}\; x = 3 where f(-2) < 0,\; \text{and}\; f(3) < 0. Better?
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  4. #19
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    <br />
y=1-x^2<br />
    <br />
y'=-2x<br />
    y'=0 => x=0
    max(0,1)
    ahh

    so if our highest point is at x=1
    then there are two values as x-+->infinty which are negative
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  5. #20
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    if
    <br />
a < \frac{1}{e}<br />
    then we have two solution

    what if it equals 0??

    there is no place for being between negative and positive
    how do you say that there is 1 solution in that case
    ??

    and
    lim ln(x)-ax=+infinity-+infinity
    x->+infinity

    its not -infinity like you said
    ??
    Last edited by transgalactic; February 15th 2009 at 07:28 AM.
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