Tangent Plane & normal line . Advanced calculus.pdf
https://www.youtube.com/watch?v=YOlukI-Ppqk
the tangent plane and normal line are concepts used to describe the behavior of a function at a specific point in three-dimensional space.
The tangent plane is a flat surface that touches the function at a specific point, and is tangent to the surface at that point. This means that the tangent plane has the same slope as the surface at that point. The tangent plane is useful for approximating the behavior of the function near the point of tangency.