7.3 Heavy Metal(#differentiation)

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, 3, 2) is 100°C.

(a) Derive a function T(x, y, z) that gives the temperature in the ball at the point

(x, y, z).

(b) Find the rate of change of T at (1, 3, 2) in the direction toward the point (0,4, 2).

(c) Show that at any point in the ball the direction of greatest increase in temper-

ature is given by a vector that points toward the origin.