The temperature T in a ball is inversely proportional to the distance from the center of the ball which we take to be the origin. The temp at the pt 1,2 ,2) is 120 C. 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?

Question

The temperature T in a ball is inversely proportional to the distance from the center of the ball which we take to be the origin. The temp at the pt 1,2 ,2) is 120 C.  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?

anonymous · Answer

I found the rate of change of T = 360/(x^2+y^2+z^2)^(3/2) <-x,-y,-z>

anonymous · Answer

I know the greatest increase should have the same direction as T