If i need to describe how the direction of grad(f) (for a specific f) varies in space by considering grad(f) on surfaces given by f(x,y,z)=constant, how do I do this? What is the question asking? What relevence does grad(f) on a surface f(x,y,z)=constant have?
Any hints or tips appreciated
Thanks for your reply. If f(x,y,z) = x^2+y^2 for instance what can be said about how the direction of grad(f) varies in space (by considering surfaces where f=constant)?
I don't think it is sufficient to just say that for points on any surface f=constant, gradf will be normal to the surface. What else can be said?