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Unformatted text preview: ( a , b ) is a critical point ( f x ( a , b )= 0 and f y ( a , b )= 0) we deﬁne a number D to be D = f xx ( a , b ) · f yy ( a , b )-[ f xy ( a , b )] 2 Then, 1. If D ( a , b ) > 0 and f xx ( a , b ) < 0 then f has a at ( a , b ) . 2. If D ( a , b ) > 0 and f xx ( a , b ) > 0 then f has a at ( a , b ) . 3. If D ( a , b ) < 0 then f has a at ( a , b ) . 4. If D ( a , b ) = 0 then no conclusion can be made about f ( a , b ) . 8 c ± Kendra Kilmer April 23, 2009 Example 4: Find all critical points and determine whether each is a saddle point, local max, or local min. a) f ( x , y ) =-x 2-y 2 + 6 x + 8 y-21 b) f ( x , y ) = x 3 + y 3-6 xy Section 8.3 Homework Problems: 3,7,9,13,19,21,29 9...
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This note was uploaded on 03/27/2012 for the course MATH 142 taught by Professor Drost during the Fall '08 term at Texas A&M.
- Fall '08