Gradient vector to a surface; tangent plane
If is a function of three variables and the number is in the range of , then the equation defines a level surface of . If the point is on a level surface of , then the gradient of at , denoted , is perpendicular to that level surface. We can now find the plane tangent to the surface at by identifying the unique plane through that is normal to the vector .
In this interactive figure, define a function and fix a level surface of that function. Then, place point on the surface and you can view the gradient vector and tangent plane at that point.
Developed for use with Thomas' Calculus, published by Pearson.