A Counterexample: Partial Derivatives Exist but Differentiability Fails

This GeoGebra example uses geometric construction to illustrate the phenomenon that partial derivatives can exist at a point while the function is not differentiable there. The key concepts are partial derivatives, differentiability, and how local “smoothness” properties may differ across coordinate directions. Construction focus: employing the IntersectPath command to compute intersections among the paths/objects f, h, g, p, i, j, thereby identifying the crucial points or curve relations used to visualize the counterexample’s geometry. Suitable for calculus instruction and for learners studying the distinction between existence of partial derivatives and overall differentiability, including teaching with counterexamples.