# Rate of Change

• May 20th 2008, 07:13 PM
wik_chick88
Rate of Change
The temperature T in a metal disc in inversely proportional to the distance from the center of the disc, which we take to be the origin. The temperature at the point (1,2) is 10 centigrade.
(a) show that at any point the direction of greatest increase in temperature is given by a vectore that points toward the origin.
(b) find the rate of change of T at (1,2) in the direction toward the point (2,1)

I have no idea about (a), and with (b), isnt the rate of change undefined, because rate of change of distance = 0 (distance of both points to the origin are the same = sqrt (5)) and thus (rate of change of T)/(rate of change of D) is undefined??? soooooo confused!! Please help!!!
• May 20th 2008, 07:34 PM
TKHunny
Quote:

Originally Posted by wik_chick88
The temperature T in a metal disc in inversely proportional to the distance from the center of the disc, which we take to be the origin.

$\displaystyle T(x,y) = \frac{k}{\sqrt{x^{2}+y^{2}}}$?

• May 21st 2008, 04:20 PM
wik_chick88
Rate of Change
definitely sure that it is centigrade. do you then sub in the point (1,2) and T=10 to find k??
• May 22nd 2008, 10:01 AM
TKHunny
That's a good start.

How about the "direction of greatest increase in temperature" after that?
• May 22nd 2008, 04:39 PM
wik_chick88
Rate of Change
yes well ive found k = 10sqrt(5), so then do i just have to explain that as the magnitude of the vector (which is sqrt(x^2+y^2)) decreases, the temperature increases? or do i actually have to show it mathematically?

and what about the second part of the question? is the rate of change just 0 because the distance to the origin doesnt actually change thus neither does the temperature???
• May 22nd 2008, 07:50 PM
asw-88
I can be of no help, but if you figure it out can you put it up.
• May 22nd 2008, 08:35 PM
TKHunny
You are very much discouraging me. You must know something about partial derivatives. Maybe a gradient? What section are you studying?