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Math Help - Maximum and Minimum

  1. #1
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    Maximum and Minimum

    Hey.
    I need to find maximum and minimum for this function, as you can see, I found (0,0) as a "suspicious point" (I don't know how it's called in English ).
    My question is, how can I determine if it's Max or Min (if it's possible)?
    I know the test of the second derivative, but how should I get it? I mean should I use the definition of the derivative because I think there is a problem around the point (0,0).
    Any idea guys?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by asi123 View Post
    Hey.
    I need to find maximum and minimum for this function, as you can see, I found (0,0) as a "suspicious point" (I don't know how it's called in English ).
    My question is, how can I determine if it's Max or Min (if it's possible)?
    I know the test of the second derivative, but how should I get it? I mean should I use the definition of the derivative because I think there is a problem around the point (0,0).
    Any idea guys?
    This has a maximum at (0,0) it is a critical point as the derivative does not exist there. You need only obsever that for any (x,y) \ne (0,0), \sqrt{x^2+y^2}>0 and so z(0,0) must be a maximum.

    ( z(x,y) is smooth everywere else and there are no critical points way from (0,0) so there are no other maxima or minima, the surface is in fact a cone with vertex at (0,0) )

    RonL
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