The first step in this demo is to choose a function f(x, y, z) and some point P at which to test the differentiability of f. Next, choose some small ε that will determine the hypercones which must be the bounds of the function for some δ in order for the function to be differentiable. Now, examine each slice through point P by rotating the slice plane in the "Plane Orientation" window (do this by rotating the normal to the plane). If you find some orientation for which the slice of the function passes through the slice cones, try making δ smaller.