This preview shows page 1. Sign up to view the full content.
Unformatted text preview: b) An example of a 4-saddle is f ( x,y ) = xy ( y 2-x 2 ); an n-saddle is g ( x,y ) = ( y-x )( y-1 2 x )( y-1 3 x ) ( y-1 n x ). B5. a) (0 , 0) is a saddle point so the level curves near (0 , 0) are hyperbola. ( b, b ) are both local minima and so the level curves near both these points are ellipses. B6. k 1, (0 , 0) is a global max, no local or global min. 0 < k < 1 (0 , 0) is a local min all pointson x 2 + y 2 = 1-k are global max. No global min. k < 0, (0 , 0) is a global min, all points x 2 + y 2 = 1-k are global max. B7. i) f ( x,y ) = 2( x-1 2 y ) 2 . The critical points y = 2 x are all local minimums. ii) f ( x,y ) = p | 1-x 2-y 2 | . The critical points x 2 + y 2 = 1 are all local minimums, (0 , 0) is a local maximum. 1...
View Full Document
This note was uploaded on 04/18/2010 for the course MATH 237 taught by Professor Wolczuk during the Spring '08 term at Waterloo.
- Spring '08