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Math Help - Please check my critical points

  1. #1
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    Please check my critical points

    Find the critical points of the equation xy-7x^2y-9xy^2
    The critical points I found in increasing lexicographic order are
    (0.0) (0,1/9),(1/21,1/27) and (1/7, 0)
    at (0,0) is it undefined
    at (0/1/9) and (1/7,0) you have saddle points
    at (1/21,1/2) you have a local max.
    Is this correct?
    Thank you
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  2. #2
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    Quote Originally Posted by koalamath View Post
    Find the critical points of the equation xy-7x^2y-9xy^2
    The critical points I found in increasing lexicographic order are
    (0.0) (0,1/9),(1/21,1/27) and (1/7, 0)
    at (0,0) is it undefined Mr F says: ?? Do you mean the test fails? {\color{red}xy-7x^2y-9xy^2} is certainly not undefined at (0, 0) ....

    at (0/1/9) and (1/7,0) you have saddle points
    at (1/21,1/2) you have a local max.
    Is this correct?
    Thank you
    ..
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  3. #3
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    fxx=-14y
    fxx(0,0)=0
    doesn't that make it undefined?
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  4. #4
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    Quote Originally Posted by koalamath View Post
    fxx=-14y
    fxx(0,0)=0
    doesn't that make it undefined?
    Why? What part of the second partial derivative test says this? How can z = xy-7x^2y-9xy^2 be undefined when x = 0 and y = 0? z = 0, a perfectly well defined value.

    In fact, there's a saddle point at (0, 0, 0).

    I haven't checked your other answers.
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  5. #5
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    ohhhh now i see it
    D is less than 0 at (0,0)
    I didn't see the negative
    thank you so much
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