Tangent Plane to Surface
Loading the math board and drawing, please wait…
This example demonstrates constructing the tangent plane to a surface defined by a function f(x, y) at a given point. Key mathematical concepts include partial derivatives and tangent planes. GeoGebra commands used include Vector and Derivative. Suitable for university calculus courses.
GeoGebra Commands & Parameters
Vector((hx, 0, f(hx, 0))) → uVector((0, hy, f(0, hy))) → vDerivative(f, x) → fxDerivative(f, y) → fy
AI Drawing Prompt Reference
Draw a 3D surface defined by a function of two variables. At a selected point on the surface, construct two tangent vectors along the x- and y-directions, each lying in the surface's tangent lines. These two vectors span the tangent plane at that point. Also indicate the partial derivatives with respect to x and y, showing how they determine the plane's orientation. The figure should clearly show the surface, the two tangent vectors, and the tangent plane in space.
The prompt above was compiled from the original drawing commands and is for reference only.