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Thread: I need help founding Extrema of a Function

  1. #1

    Lightbulb I need help founding Extrema of a Function

    Hey Guys I hope All is fine ? Please I need Helping getting the points critiques And if it's minimum or maximum

    Function : f(x;y) = xlny-ylnx
    Thanks


  2. #2
    Elite Member
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    Quote Originally Posted by spynet201 View Post
    Hey Guys I hope All is fine ? Please I need Helping getting the points critiques And if it's minimum or maximum

    Function : f(x;y) = xlny-ylnx
    Thanks
    What are your thoughts?

    Please share your work with us ...even if you know it is wrong.

    If you are stuck at the beginning tell us and we'll start with the definitions.

    You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

    http://www.freemathhelp.com/forum/announcement.php?f=33
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  3. #3

    Exclamation this is what i get but in the exercice rule i must get extrema min or max so someting

    f(x,y)=xlog(y)ylog(x)
    we'll do it the long way first and then use a shortcut

    fx=log(y)yx

    fy=xylog(x)

    set these both equal to zero and solve

    log(y)=yx

    log(x)=xy

    The only solution to this is x=y=e

    The shortcut is knowing that in symmetric expressions like this extrema always occur when y=x

    If we set y=x we can immediately see log(x)=xx=1

    x=e

    To characterize this critical point we first look at

    D=fxxfyyf2xy at the critical point

    fxx=yx2

    fyy=xy2

    fxy=1y1x

    D=fxxfyyf2xy(x,y)=(e,e)=(1y1x)21xy(x,y)=(e,e)1e2

    D<0 and thus this critical point is a saddle point.

  4. #4
    Elite Member stapel's Avatar
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    Cool

    Quote Originally Posted by spynet201 View Post
    this is what i get but in the exercice rule i must get extrema min or max so someting...

    f(x,y)=xlog(y)ylog(x)
    we'll do it the long way first and then use a shortcut....
    Do you perhaps mean, "This is what somebody else gave me in reply to another of my posts of this question, but he didn't give me everything I need for my hand-in homework, so you guys finish it for me"...?

    How about you at least go to the effort of telling us how your book defines "the points critiques". Thank you!

  5. #5
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    I'm a bit late to the thread it seems, but this exact question was also posted right here on this forum. If the original poster is actually interested in doing work for themselves, the hints provided there will hopefully be of some use.

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