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Math Help - ABS Max and Min

  1. #1
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    ABS Max and Min

    Find the absolute maximum and absolute minimum of the function f(x)=ln(3x)/x on the interval [0.1, 5]
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    Quote Originally Posted by Shivian View Post
    Find the absolute maximum and absolute minimum of the function f(x)=ln(3x)/x on the interval [0.1, 5]

    Derivate and put f'(x)=0 to find candidates to be the maximum.

    Tonio
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  3. #3
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    Is this correct?

    x=(e^9)-3
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  4. #4
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    Quote Originally Posted by tonio View Post
    Derivate and put f'(x)=0 to find candidates to be the maximum.

    Tonio
    He will also need to check the boundary points.
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  5. #5
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    Quote Originally Posted by Bruno J. View Post
    He will also need to check the boundary points.

    Of course. Thanx for the clarification.

    Tonio
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    Quote Originally Posted by Shivian View Post
    Is this correct?

    x=(e^9)-3

    I don't think so. What's the derivative of your function, anyway?

    Tonio
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  7. #7
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    Here is all I have so far.

    Interval: [0.1, 5]
    f(x)=ln(3x)/x
    f1(x)=(1-ln(3x))/(x^2)
    x=e/3

    f(.1)=-12.0397
    f(5)=0.5416
    f(e/3)=1.1036

    Max is f(e/3)=1.1036
    Min is f(.1)=-12.0397

    How close am I?
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  8. #8
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    Quote Originally Posted by Shivian View Post
    Here is all I have so far.

    Interval: [0.1, 5]
    f(x)=ln(3x)/x
    f1(x)=(1-ln(3x))/(x^2)
    x=e/3

    f(.1)=-12.0397
    f(5)=0.5416
    f(e/3)=1.1036

    Max is f(e/3)=1.1036
    Min is f(.1)=-12.0397

    How close am I?
    So close that you already are there: I see no mistake in the above at all.
    Way to go!

    Tonio
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