Here goes:

The temperature T in a metal ball is inversely proportional to the distance from the center of the ball, which we take to be the origin. The temperature at the point (1,2,2) is $\displaystyle 120^{\circ}$.

(a) Find the rate of change of T at (1,2,2) in the direction toward the point (2,1,3).

(b) Show that at any point in the ball the direction of greatest increase in temperature is given by a vector that points toward the origin.