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 $ 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.
Partial Derivatives
Directional Derivatives and the Gradient…