Thread: directional derivative

The temperature at the point (x, y, z) in space is given by T(x, y, z) = x + yz. A fly is at the point (1, 2, 1). In what direction should he begin to fly to cool off as quickly as possible?

Hey apatite.

If the fly wants to cool off in the best way then the derivative with respect to the temperature must be minimal. What does this imply?

Originally Posted by apatite

The temperature at the point (x, y, z) in space is given by T(x, y, z) = x + yz. A fly is at the point (1, 2, 1). In what direction should he begin to fly to cool off as quickly as possible?

Actually points in the direction of most rapid decrease in the field determined by .

Recall that .