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Math Help - multivariable critical point

  1. #1
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    multivariable critical point

    Show that z=(x+y)^2 has infinity many critical points.
    I've got the formula of the tangent plane to be z=(a+b)(2x+y2-a-b) where a and b are the points they touch the surface, so they too are variables.
    Last edited by superdude; September 24th 2009 at 07:54 PM.
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by superdude View Post
    Show that z=(x+y)^2 has infinity many critical points.
    I've got the formula of the tangent plane to be z=(a+b)(2x+y2-a-b) where a and b are the points they touch the surface, so they too are variables.
    If you set the partial derivatives equal to zero, as a system, you should see that there are infinitely many solutions.

    \frac{dz}{dx} = 2(x+y) = 0
    \frac{dz}{dy} = 2(x+y) = 0

    It's the set of all points 3-dimensional space such at x=-y.
    I hope this helps.
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