(A)Let $f ( x , y ) = x ^ { 2 } - 4 x y + 2 y ^ { 2 }$

question 14

Essay

(a)Let $f ( x , y ) = x ^ { 2 } - 4 x y + 2 y ^ { 2 }$ .Find the maximum and minimum values of f on the curve $x ^ { 2 } + 2 y ^ { 2 } = 1$
(b)Use the results of part (a)to find the maximum and minimum values of $h ( x , y ) = e ^ { x ^ { 2 } - 4 x y + 2 y ^ { 2 } }$ on the curve $x ^ { 2 } + 2 y ^ { 2 } = 1$ Explain your work.

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Definitions:

Cognitive Ethology

A branch of ethology that studies the mental experiences of animals, particularly their cognitive processes and natural behaviors.

Nonhuman Animals

Living organisms that are not classified as human beings, including all species within the animal kingdom except Homo sapiens.

Cognitive Processes

Mental activities involved in acquiring, storing, retrieving, and using knowledge, such as perception, memory, and reasoning.

Tacit Knowledge

Knowledge that is difficult to transfer to another person by writing it down or verbalizing it, often acquired through personal experience.