Question

Find a vector pointing in the direction of greatest increase of temperature at (1,-1,1).

what's the idea of the question? finding the directional derivative of the temperature function at that particular point?

Answer 1

temperature must be function of position x,y,z

gradient gives the maximum rate of change along with the maximum rate of change,

gradient of T is a vector, take dot product with the unit position vector, you should get the directional derivative

Answer 2

*along with the direction of maximum rate of change,

Answer 3

so this question is asking for, directional derivate? my english is not so good.. D; cannot understand the question lol

Answer 4

I guess ... find some vector along the maximum rate of change ... would be to find gradient of temperature

Answer 5

thx