# directional derivative

• February 14th 2013, 09:56 AM
apatite
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?
• February 14th 2013, 03:21 PM
chiro
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?
• February 14th 2013, 03:57 PM
Plato
Re: directional derivative
Quote:

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