This is a problem thats been bugging me. Suppose you are on the surface M(x,y)=3*x^2+y^2+5000 that describes a magnetic field, you are at the point (8,6), what is the curve along which you should travel so as to minimize field intensity as rapidly as possible? I am told I need to solve a differential equation, I am thinking I need to find the minimal directional derivative and somehow from that find the equation of the line that represents, and integrate it to get a curve. But I am at a loss as to how to start. Someone help?