Suppose That (1, -4)is a Critical Point of a Smooth $f ( 1 , - 4 ) = - 1 , f _ { x x } ( 1 , - 4 ) = 2 , f _ { x y } ( 1 , - 4 ) = 2 , f _ { y y } ( 1 , - 4 ) = - 3$

question 25

Essay

Suppose that (1, -4)is a critical point of a smooth function f(x, y)with $f ( 1 , - 4 ) = - 1 , f _ { x x } ( 1 , - 4 ) = 2 , f _ { x y } ( 1 , - 4 ) = 2 , f _ { y y } ( 1 , - 4 ) = - 3$ Find the quadratic approximation of f at (1, -4).

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