Consider the paraboloid z=f(x,y)= 4+x^2+3y^2 . Beginning at (3,4,61) on the surface, find the path in the xy-plane that points in the direction of steepest descent on the surface.

Question

anonymous · Answer

Take the gradient?

anonymous · Answer

Gradient = <2x, 6y>

Your vector:  6i + 24j

@AccessDenied  help!  I thought I remembered all of this :-(

anonymous · Answer

When they say "path" are they looking for the equation of the line or do they want the vector?

accessdenied · Answer

i was imagining that the path on xy-plane was something like this with respect to an actual function:
|dw:1333233857061:dw|

that's just from intuition tho, i havent actually gotten into this part of calc -- i was just curious to see the answer.  D: