Maximal Directional Derivative Visualization

This GeoGebra example demonstrates the concept of directional derivative on a surface in 3D space, highlighting the direction in which the rate of change is maximal. It visually connects the gradient vector to the steepest ascent direction on a surface. Core mathematical concepts include directional derivatives, gradient, maximum rate of change, and the geometric relationship between vectors and tangent planes. The construction uses commands such as PointIn to place a point on the surface, Derivative to compute derivatives, Vector and Plane to define direction vectors and tangent planes, and Angle to measure angles. Dynamic text objects display numerical values. This resource is suitable for university-level calculus or multivariable function courses, as well as advanced high school mathematics, to illustrate the geometric meaning of gradient and directional derivatives.