Suppose That (0, -2)is a Critical Point of a Smooth $f ( 0 , - 2 ) = - 2 , f _ { x x } ( 0 , - 2 ) = - 1 , f _ { x y } ( 0 , - 2 ) = 2 , f _ { y y } ( 0 , - 2 ) = - 5$

question 74

Essay

Suppose that (0, -2)is a critical point of a smooth function f(x, y)with $f ( 0 , - 2 ) = - 2 , f _ { x x } ( 0 , - 2 ) = - 1 , f _ { x y } ( 0 , - 2 ) = 2 , f _ { y y } ( 0 , - 2 ) = - 5$ What can you conclude about the behavior of the function f near (0, -2)?

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