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Math Help - Maximum Value

  1. #1
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    Maximum Value

    Find the maximum value of:

     f(x) = x^2 ln(1/x)
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  2. #2
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     \frac{d}{dx} x^{2}\ln \Big(\frac{1}{x}\Big) = 2x \ln \Big(\frac{1}{x}\Big) +x^{2}*\frac{1}{1/x}\Big(\frac{-1}{x^{2}}\Big) = 2x \ln \Big(\frac{1}{x} \Big) -x

     2x \ln \Big(\frac{1}{x} \Big) -x = 0

     \ln \Big(\frac{1}{x} \Big) = \frac{1}{2}

     x = \frac{1}{e^{1/2}}
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  3. #3
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    Quote Originally Posted by penguinpwn View Post
    Find the maximum value of:

     f(x) = x^2 ln(1/x)
    Make life a bit easier by noting that f(x) = - x^2 \ln (x). Now apply the product rule.
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    Quote Originally Posted by mr fantastic View Post
    Make life a bit easier by noting that f(x) = - x^2 \ln (x). Now apply the product rule.
    Does that property of ln work with all inverses?

    for example, would f(x) = ln (cscx)be equal to f(x) = ln (sinx)?
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  5. #5
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    Quote Originally Posted by penguinpwn View Post
    Does that property of ln work with all inverses?

    for example, would f(x) = ln (cscx)be equal to f(x) = ln (sinx)?
    You should have learned in pre-calculus that \log \frac{1}{A} = - \log A.
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