- #1
sam2
- 22
- 0
Hi all,
Came across this problem, but it has stumped me:
Let S denote the unit sphere x^2 + y^2 + z^2 = 1, and let
u = x + 2y + 3z
be temperature at points everywhere in 3-space.
Find the hottest and coldest points on the unit ball x^2 + y^2 + z^2 <= 1
I figured out that we need to clculate the partial derivatives in each 3 co-ordinate directions and need them all to be zero... while ensuring that we are in the unit ball. Is this just down to trial and error or is there a trick involved? Any hints?
Many Thanks,
Sam
Came across this problem, but it has stumped me:
Let S denote the unit sphere x^2 + y^2 + z^2 = 1, and let
u = x + 2y + 3z
be temperature at points everywhere in 3-space.
Find the hottest and coldest points on the unit ball x^2 + y^2 + z^2 <= 1
I figured out that we need to clculate the partial derivatives in each 3 co-ordinate directions and need them all to be zero... while ensuring that we are in the unit ball. Is this just down to trial and error or is there a trick involved? Any hints?
Many Thanks,
Sam