Unformatted text preview: correct. Thus, we can divide out the 2 Î» and get b 2 c 2 x 2 = a 2 c 2 y 2 = a 2 b 2 z 2 Since these are all equal, we can reduce g ( x, y, z ) = 0 to 3 b 2 c 2 x 2-a 2 b 2 c 2 = 0 from which we quickly get that x = a âˆš 3 . Similarly, we can get that y = b âˆš 3 and z = c âˆš 3 . Now, the problem asks us for the maximum volume, so we need to use these to make a volume. But note that if we just plugged these values into f , we would not get the whole volume, but rather we would get one-eighth of it (Fgure out why). Thus, the total volume is 8 f ( a âˆš 3 , b âˆš 3 , c âˆš 3 ) = 8 abc 3 âˆš 3 1...
View Full Document
This note was uploaded on 08/11/2008 for the course MATH 234 taught by Professor Dickey during the Fall '08 term at University of Wisconsin.
- Fall '08
- Vector Calculus