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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The Answer of 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).

Suppose That (1, -4)is a Critical Point of a Smooth f(1,−4)=−1,fxx(1,−4)=2,fxy(1,−4)=2,fyy(1,−4)=−3f ( 1 , - 4 ) = - 1 , f _ { x x } ( 1 , - 4 ) = 2 , f _ { x y } ( 1 , - 4 ) = 2 , f _ { y y } ( 1 , - 4 ) = - 3f(1,−4)=−1,fxx​(1,−4)=2,fxy​(1,−4)=2,fyy​(1,−4)=−3

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