Let f ( x , y ) x 2 y 2 and g ( x , y ) x 2 y 2 Verify that f ( 0 , 0 ) g ( 0 , 0 ) ( 0 , 0 ) and both Hf ( 0 , 0 ) and Hg ( 0 , 0 are positive semi definite Prove that 0 , 0 ) is a point of local minima for f but not for g Does this contradict the second order necessary or sufficient conditions for the existence of local minima

Question

Let f ( x , y )   x 2   y 2 and g ( x , y )   x 2 y 2   Verify that f ( 0 , 0 )   g ( 0 , 0 )   ( 0 , 0 ) and both Hf ( 0 , 0 ) and Hg ( 0 , 0 are positive semi   definite  Prove that 0 , 0 ) is a point of local minima for f but not for g   Does this contradict the second   order necessary or sufficient conditions for the existence of local minima

HelloExperts · Accepted Answer

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Let f ( x , y ) = x 2 + y 2 and g ( x , y ) = x 2 y 2

Step by Step Solution

1 Understanding Responsive Design Principles

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