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Math Help - Stationary values

  1. #1
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    Stationary values

    Show that x\ln x has only one stationary value, and find it.

    I differentiated the equation:
    \frac{d}{dx}(x\ln x) = x(\frac{1}{x})+ \ln x(1) = 1+\ln x
    Then
     1+\ln x=0
     \ln x=-1
    x=e^{-1}=\frac{1}{e}
    Am i correct? Because the answer is supposed to be -\frac{1}{e}
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  2. #2
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    Quote Originally Posted by arze View Post
    Show that x\ln x has only one stationary value, and find it.

    I differentiated the equation:
    \frac{d}{dx}(x\ln x) = x(\frac{1}{x})+ \ln x(1) = 1+\ln x
    Then
     1+\ln x=0
     \ln x=-1
    x=e^{-1}=\frac{1}{e}
    Am i correct? Because the answer is supposed to be -\frac{1}{e}
    The x-coordinate of the stationary point is x = 1/e. However, the question is not asking for that value, it's asking for the value of the function. And that value is obviously found by substituting x = 1/e into the given rule ....
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  3. #3
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    ok thanks! that was what i missed
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