Find the extreme values of the function f ( x , y ) = 2 ( x &#x22

glycleWogry

glycleWogry

Answered question

2022-06-23

Find the extreme values of the function
f ( x , y ) = 2 ( x y ) 2 x 4 y 4
My attempt
p = δ f δ x = 4 ( x x 3 y )
and
q = δ f δ y = 4 ( y y 3 x )
Equating p and q to 0 I get
x x 3 y = 0
and
y y 3 x = 0
I have no idea on how to solve the above 2 equations

Answer & Explanation

massetereqe

massetereqe

Beginner2022-06-24Added 21 answers

You get two equations. You get y from the first (for example) and you substitute in the second. You will get following equations:
x x 3 ( x x 3 ) 3 = x
this can be simplified and factorized in this way:
x 3 ( x 2 2 ) ( x 4 x 2 + 1 ) = 0
Now you can easily find the solutions can you? Those are just quadratic equations. For you to check the solutions will be x = 0 , 2 , 2 . Then you can take your x and substitute them in your questions to get y. This should get you going and you should be able to finish your exercise.

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