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)?

Question

Quizplus · Accepted Answer

The Answer of 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)?

Suppose That (0, -2)is a Critical Point of a Smooth f(0,−2)=−2,fxx(0,−2)=−1,fxy(0,−2)=2,fyy(0,−2)=−5f ( 0 , - 2 ) = - 2 , f _ { x x } ( 0 , - 2 ) = - 1 , f _ { x y } ( 0 , - 2 ) = 2 , f _ { y y } ( 0 , - 2 ) = - 5f(0,−2)=−2,fxx​(0,−2)=−1,fxy​(0,−2)=2,fyy​(0,−2)=−5

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