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Math Help - Absolute Extrema

  1. #1
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    Absolute Extrema

    I have a question regarding Absolute Extrema.

    f(x) = 7xlnx

    Find the absolute extrema. For the answer, my professor got 1/e. I do not understand the last step of this. He had lnx = -1 and then he turned it into
    e^lnx = e^-1, which followed x = e^-1. Is there any link with x and e ^lnx I am missing?

    Thanks
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  2. #2
    Senior Member AllanCuz's Avatar
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    Quote Originally Posted by cokeclassic View Post
    I have a question regarding Absolute Extrema.

    f(x) = 7xlnx

    Find the absolute extrema. For the answer, my professor got 1/e. I do not understand the last step of this. He had lnx = -1 and then he turned it into
    e^lnx = e^-1, which followed x = e^-1. Is there any link with x and e ^lnx I am missing?

    Thanks
    e^{ln[f(x,y)]} = f(x,y)

    by rule of logs. The base of ln is e so when we raise the base to ln, we simply get the above.
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