The temperature at a point (x,y,z) is given by T(xyz)=200e^(-x^2-(y^2/4)-(z^2/9) where T is measured in degrees Celsius and x,y, and z in meters. I found the rate of change of temp. at the point (-1,1,-1) in the direction toward the point (5,-2,5). I just dont understand these two two questions:

In which direction (unit vector) does the temperature increase the fastest at (-1, 1, -1)?

What is the maximum rate of increase of T at (-1, 1, -1)?

Question

The temperature at a point (x,y,z) is given by T(xyz)=200e^(-x^2-(y^2/4)-(z^2/9) where T is measured in degrees Celsius and x,y, and z in meters. I found the rate of change of temp. at the point (-1,1,-1) in the direction toward the point (5,-2,5). I just dont understand these two two questions:

In which direction (unit vector) does the temperature increase the fastest at (-1, 1, -1)? 

What is the maximum rate of increase of T at (-1, 1, -1)?

zepdrix · Answer

Ooooo I think I remember this exact question from one of my Calc 3 tests.
That was a long long time ago though >.<
Lemme see if I can find it.. sec.

anonymous · Answer

Okay thank you. I understand the general concept but I can't seem to find the right answer. I got 200e^(-49/36)((4/3)+(1/6)+(4/27)) for the rate of change of temp. at the point (-1, 1, -1) in the direction toward the point (5, -2, 5). And i know that that is correct.

zepdrix · Answer

Mmmm ya I remember the first part :oc Looks like you've got that figured out already though lol. I googled and found this: http://www.math.ubc.ca/~sjer/math253/s4.pdf Question 17 seems to be asking the same questions (wish solutions provided).

anonymous · Answer

Okay thank you I'll check that out and see if I can get the right answer :)