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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Enrichment

A benefit or advantage that one party gains, often at the expense of another, without offering compensation in certain legal contexts.

Quasi-contract

A legal concept where a court enforces an agreement between parties even though there is no actual contract between them, to prevent one party from being unjustly enriched.

Unjust

Not based on or behaving according to what is morally right and fair.

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A contract in which only one party makes an enforceable promise to perform an action, often in response to an act by the other party.