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?
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 $\displaystyle - \nabla f(a,b,c)$ points in the direction of most rapid decrease in the field determined by $\displaystyle f$.
Recall that $\displaystyle \nabla f = f_x i + f_y j + f_z k$.