Partial Derivatives: Geometric Interpretation of Multivariable Functions

This GeoGebra example demonstrates the geometric meaning of partial derivatives for a function of two variables. It shows how intersecting a surface with vertical planes parallel to the coordinate planes produces curves whose tangent slopes correspond to the partial derivatives with respect to x and y. Core mathematical concepts include multivariable functions, partial derivatives, tangent slopes, analytic geometry in space, and local linear approximation. The construction relies on GeoGebra commands IntersectPath, Vector, and Line, together with objects such as c, b, a, f, text1, y_0, plane1, curve1, x_0, A, u1, l1, plane2, curve2, u2, l2, PartialX, PartialY, and text2 through text6. By combining path intersection, vector construction, and line drawing, the example labels PartialX and PartialY to visualize directional rates of change. It is suitable for senior high school and university calculus instruction, serving teachers who need a dynamic demonstration of partial derivative geometry and students exploring the local behavior of surfaces.