Chapter 4.6, Problem 306E

For the following exercises, solve the problem.

306. The temperature T in a metal sphere is inversely proportional to the distance from the center of the sphere (the origin: (0. 0. 0)). The temperature at point (1. 2. 2)

is 120°C.

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

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