91- Local Linearization

Just like the normal derivative is the slope of the line tangent to the graph, in multivariate calculus we are able to find that the partial derivative with respect to some variable is the slope of the tangent plane along the direction of the variable we want.

For an implicitly defined surface at some point , th etangent plane to the graph is defined as For an explicitly defined surface at some point , the plane tangent to the graph is defined as