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Math Help - For what values...

  1. #1
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    Question For what values...

    For what values of a and b will the function defined by f(x)=a(x-b ln x)

    have f(2)=5 as arelative minimum value.Justify your conclusion.
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  2. #2
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    Quote Originally Posted by mathcalculushelp View Post
    For what values of a and b will the function defined by f(x)=a(x-b ln x)

    have f(2)=5 as arelative minimum value.Justify your conclusion.
    first 2 is a relative minimum for the function that mean it is a critical point for the first derivative

    f(x)=a(x-b\ln x)

    f'(x) = a-\frac{ab}{x}

    f'(2) = a-\frac{ab}{2} = 0 \Rightarrow b=2

    and you have f(2)=5

    f(2) = 2a -ab\ln(2) =5

    2a-a(2)\ln(2) =5 \Rightarrow a=\frac{5}{2-2\ln (2)}
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