Unformatted text preview: b) An example of a 4saddle is f ( x,y ) = xy ( y 2x 2 ); an nsaddle is g ( x,y ) = ( yx )( y1 2 x )( y1 3 x ) Â·Â·Â· ( y1 n x ). B5. a) (0 , 0) is a saddle point so the level curves near (0 , 0) are hyperbola. ( Â± b, Â± b ) are both local minima and so the level curves near both these points are ellipses. B6. k â‰¥ 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 = 1k are global max. No global min. k < 0, (0 , 0) is a global min, all points x 2 + y 2 = 1k are global max. B7. i) f ( x,y ) = 2( x1 2 y ) 2 . The critical points y = 2 x are all local minimums. ii) f ( x,y ) = p  1x 2y 2  . The critical points x 2 + y 2 = 1 are all local minimums, (0 , 0) is a local maximum. 1...
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 Spring '10
 WILKIE
 Math, Critical Point, Max

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