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Math Help - Fam. of func.

  1. #1
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    Fam. of func.

    need some help on finding the critical value and x intercept of this equation:

    y(x) = ax-xln(x)

    thanksness
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  2. #2
    Junior Member teuthid's Avatar
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    the x-intercept is the x_0 such that y(x_0)=0. so...

    0=ax-x\ln x

    \rightarrow ax=x\ln x

    \rightarrow a = \ln x

    \rightarrow x=e^{a}

    so the x-intercept of this function is (e^{a},0).

    What's the definition of a critical value? I'm not familiar with that term.
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by mathlete View Post
    need some help on finding the critical value and x intercept of this equation:

    y(x) = ax-xln(x)

    thanksness
    A critical value would be a value where the first derivative of the function is 0 or where the function does not exist.

    So the function does not exist at x = 0, so this is a critical point.

    y^{\prime}(x) = a - ln(x) - 1

    So when this is 0 we have a critical point:
    a - ln(x) - 1 = 0

    ln(x) = a - 1

    x = e^{a - 1}

    So this is your other critical point.

    -Dan
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