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Unformatted text preview: counter-example.) (a) If f has a local maximum at the point a , then f cannot have a local minimum at a . (b) If a is a saddle point of f , then f cannot have a local extremum at a . (To see the deﬁnition of a saddle point, please read Example 1 on p.246 and the description in lines 1–2 on p.247 of textbook.) (c) If f has a local minimum at a and g has a local maximum at a , then a is a saddle point of f + g . 4. Identify and determine the nature of the critical points of the functions f ( x,y ) = 2 x 3-6 xy + 3 y 2 . 5. ( § 4.3 no.6) Use Lagrange multipliers to identify the critical points of f ( x,y,z ) = x 2 + y 2 + z 2 subject to the constraint x + y-z = 1. (Note: Here you are not required to characterize the critical points you found.) 1...
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- Spring '11
- Multivariable Calculus