A Non-Differentiable Surface
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This animation depicts a standard surface from multivariable calculus.
(See notes below.)
The surface shown here is given by the equation
z = √|x y|. This surface is continuous at the origin and both of its
first order partial derivatives are defined there. (That is, each of the curves in which
the surface intersects the vertical coordinate planes has a tangent line at
the origin.) Nevertheless,
the function is not differentiable there. (The surface has no tangent plane
at the origin.)
See
Another Non-Differentiable Surface.
(11/27/07)