 #1
 54
 4
Homework Statement:
 Suppose there is a rectangular metal plate in the Oxyplane with vertices (1,1),(5,1),(1,3) and (5,3). There is a heat source at the origin that heats the plate. Suppose the temperature at a point in the plate is inversely propotional to the distance of this point to the origin. Suppose there is an ant at the point (3.2). In which direction should the ant creep such that it gets to the cooler place fastest?
Relevant Equations:

Duf(x,y)=∇f(x,y)⋅u
To Maximizing The Directional Derivative : Duf(x,y)=∇f(x,y) , in the direction as ∇f(x,y)
For my understanding, to move to the coolest place, it has to move in direction of ∇f(x,y)
How can I find the value of 'k' to evaluate the directional derivative and what can I do with the vertices given.
How can I find the value of 'k' to evaluate the directional derivative and what can I do with the vertices given.