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Geometric interpretation for d²f/dxdy

  1. Jun 13, 2014 #1
    If the following integral:
    $$\\ \iint\limits_{a\;c}^{b\;d} f(x,y) dxdy$$ represents:

    attachment.php?attachmentid=70578&stc=1&d=1402650671.png

    So which is the geometric interpretation for ##f_{xy}(x_0, y_0)## ?
     

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  2. jcsd
  3. Jun 14, 2014 #2
    Would it be the rate of change of z with area, dz/dA at x0, y0?
     
  4. Jun 14, 2014 #3
    Yeah! But which is the geometric interpretation?
     
  5. Jun 14, 2014 #4
    I am taking my last guess back. If A is the shaded area
    f(x,y) = dA/dR
    So df/dR is a measure of the curvature. When it is zero the area A is flat.
     
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