# Math Help - directional derivative

1. ## 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?

2. ## Re: directional derivative

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?

3. ## Re: directional derivative

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 $- \nabla f(a,b,c)$ points in the direction of most rapid decrease in the field determined by $f$.

Recall that $\nabla f = f_x i + f_y j + f_z k$.