Differentiability Pathology

Last crawled date: 5 years, 10 months ago

This is a model of the graph of a function f(x,y) with the property that every directional derivative D_u f exists at the origin, but f is not differentiable at the origin. The tangent line indicator shows that all directional derivatives exist, but it is clear that there is no tangent plane.
The formula for f(x,y) is given below:
f(x,y) = r sin(3 theta) = (3 x^2 y - y^3) / (x^2 + y^2)